(It is not always "good form" to generate intermediate results in Let us now take a mental ride on a merry-go-roundspecifically, a rapidly rotating playground merry-go-round (Figure 6.25). You are using an out of date browser. A person standing next to the merry-go-round sees the ball moving straight and the merry-go-round rotating underneath it. Uniform circular motion means that a particle is traveling in a circular path at constant speed. weight vector parallel and perpendicular to the road - after all, Determine the minimum angle at which a frictionless road should be banked so that a car traveling at 20.0 m/s can safely negotiate the curve if the radius of the curve is 200.0 m. Determine the velocity that a car should have while traveling around a frictionless curve of radius 100m and that is banked 20 degrees. A curve on a highway is banked. expression given above for v would reduce to the same expression we Low pressure at the surface is associated with rising air, which also produces cooling and cloud formation, making low-pressure patterns quite visible from space. Solution. When taking off in a jet, most people would agree it feels as if you are being pushed back into the seat as the airplane accelerates down the runway. free-body diagram for the car on the banked turn is shown at left. path - so it makes sense to resolve the vectors horizontally and The rotation of tropical cyclones and the path of a ball on a merry-go-round can just as well be explained by inertia and the rotation of the system underneath. vertical components (the blue vectors). The free body diagram is a sketch of the forces on an object, or the causes of motion. The force of friction keeping the car from slipping down the curve acts opposite the component of gravity parallel to the track. You know from experience that the faster you go the more force you need to turn. Any kind of force can satisfy these conditions, which together are called the centripetal condition. To be clear, it wasn't just a nitpick. Velocity, Radius, and Period Formula - Circumference of Circle10. Therefore, you want to pick a coordinate system with one axis horizontally inward and not along the incline to match the actual direction of a. Now, in the horizontal This video contains plenty of examples and practice problems.My E-Book: https://amzn.to/3B9c08zVideo Playlists: https://www.video-tutor.netHomework Help: https://bit.ly/Find-A-TutorSubscribe: https://bit.ly/37WGgXlSupport \u0026 Donations: https://www.patreon.com/MathScienceTutorYoutube Membership: https://www.youtube.com/channel/UCEWpbFLzoYGPfuWUMFPSaoA/joinHere is a list of topics:1. Instead, there is a force to the right on the car to make it turn. 5 ) At a speed that is too large, a car would slide off the top. Velocity will allow you to calculate the inward acceleration due to those forces and therefore does not show up on the FBD. Any force or combination of forces can cause a centripetal or radial acceleration. You may use whichever expression for centripetal force is more convenient. He encounters a banked-curved area of the forest with a radius of 50m, banked at an angle of 15. Minimum Speed of Roller Coaster - Physics Problems22. An acceleration must be produced by a force. The lift force, due to the force of the air on the wing, acts at right angles to the wing. check. The bank angle has to be carefully cho. The curve has a radius \(\displaystyle r\). In this case, inward means horizontally in. An 738-kg car negotiates the curve at 93 km/h without skidding. Anyway that's not relevant just trying to give you a reference point. . Explain why the bug is more likely to be dislodged when the wipers are turned on at the high rather than the low setting. Maximum Speed Without Losing Contact With The Road - Radius of Curvature Given \u0026 Normal Force Equation21. Gravity and the vertical component of friction both act down, or in the negative direction. coming up, so I think I can forgive myself for getting the units Why isnt buoyant force included on the free body diagram. Jan 19, 2023 OpenStax. use? Likewise, fr makes a smaller angle with the x axis than it does with the y axis. Thus F g sin = F f. Also, since the car is on the verge of slipping, F f = F N where F N is the normal force. If the speed is less than this, friction is needed to counteract gravity. is friction's contribution to the centripetal force. (d) Wind flowing away from a high-pressure zone is also deflected to the right, producing a clockwise rotation. The banking angle between the road and the horizontal is Banked Curves When a car travels along a horizontal curve, the centripetal force is usually provided by the force of friction between the cars tires and the roads surface. In the first case static friction acts, since the car would travel to the outside of the curve and eventually leave the roadway if it were traveling in a straight line. toward the center of the circle) in order to help. Submit Your Ideas by May 12! The first turn on the course is banked at 15 degree, and the car's mass is 1450 kg. The following animation shows the difference between the two. The car on this banked curve is moving away and turning to the left. the turns at Talladega Motor Speedway at about 200 mi/hr. The curve is banked 7.1o from the horizontal and is rated at 35 mph. Remember than an inward force is required in order to make an object move in a circle. No further mathematical solution is necessary. straightened out at this point. Want to cite, share, or modify this book? velocity from Example 1. then you must include on every physical page the following attribution: If you are redistributing all or part of this book in a digital format, 0. The math to solve a 2nd Law problem is always easier if you pick one axis along the direction of acceleration. Coefficient of Restitution - definition, formula, numerical, Normal Force - for horizontal surface and inclined plane with formula, Numerical problems based on the inclined plane physics solved, Multiple Choice Questions on Motion physics (MCQs on motion). Noninertial (accelerated) frames of reference are used when it is useful to do so. Physics 02-07 Centripetal Force and Banked Curves Name: _____ Created by Richard Wright - Andrews Academy To be used with OpenStax College Physics Homework 1. Help Albo with the following: 15" a. It seems there is a velocity for each angle at which there is no friction. How to calculate the mass of the sun29. The flat curve at the beginning of the video needs a static frictional force to satisfy the centripetal condition, as that is the only force acting in the horizontal direction of the curve radius. We can now find the bank angle by looking at the x force equation: Example 2. Continue down to step 2 when you are ready to continue. If the radius of the curve is 10 meters and the streetcar speed is 5 km/h, what angle with respect to the vertical will be made by hand straps hanging from the ceiling of the streetcar? Race tracks for bikes as well as cars, for example, often have steeply banked curves. a. In this case, the x-component of fr is adjacent to the 7.1oangle and so is given by fr cos(7.1o) as shown. Assuming the base of the track is on the x-z plane, you can create a triangle by taking a cross section pointing radially inward from the circle pointing in the positive y direction. Tension Force of Tetherball Given Length and Period16. Centrifugal force is a commonly used term, but it does not actually exist. force to turn the car: Suppose you want to negotiate a curve with a radius of 50 meters Circular Motion Force Problem: Banked Curve A 540 kg car is merging onto the interstate on a banked curve. consent of Rice University. What is the speed \(\displaystyle v\) at which the car can turn safely? force, N (blue components) and the friction force, f (red components) Since the net force in the direction perpindicular to the car is 0, F N = F g cos . (a) The car driver feels herself forced to the left relative to the car when she makes a right turn. This gives the equation or formula of the Banking angle. You are asked to design a curved section of a highway such that, when the road is icy and the coefficient of static friction is 0.08, a car at rest will not slide down the curve slope and, if the car is traveling at 60 km/h or less it will not slide to the outside of the curve. parallel to the incline, so it made sense to have the vectors Particles in the fluid sediment settle out because their inertia carries them away from the center of rotation. The driver turns the steering wheel to negotiate the curve. This year you'll learn what makes physics so interesting.and cool! acceleration is horizontal - toward the center of the car's circular ft. that are banked at 33o (source). If a car takes a banked curve at less than the ideal speed, friction is needed to keep it from sliding toward the inside of the curve (a problem on icy mountain roads). What sideways frictional force is required between the car and the road in order for the car to stay in its lane? For a better experience, please enable JavaScript in your browser before proceeding. (b) Without the Coriolis force, air would flow straight into a low-pressure zone, such as that found in tropical cyclones. This physics video tutorial explains the concept of centripetal force and acceleration in uniform circular motion. Question: Civil engineers generally bank curves on roads in such a manner that a car going around the curve at the recommended speed does not have to rely on friction between its tires and the road surface in order to round the curve. Passengers instinctively use the car as a frame of reference, whereas a physicist might use Earth. What g force is the pilot experiencing? This implies that for a given mass and velocity, a large centripetal force causes a small radius of curvaturethat is, a tight curve, as in Figure 6.20. I do not wish to restart the conversation of whether a mass "on the verge of slipping" is slipping or not. In an "ideally banked curve," the angle size 12{} {} is such that you can negotiate the curve at a certain . The force equation for the y direction is. (a) A rider on a merry-go-round feels as if he is being thrown off. A banked curve is a turn in which the driving surface is not horizontal. Neglect the effects of air drag and rolling friction. Remember than an inward force is required in order to make an object move in a circle. The curve is banked 7.1 o from the horizontal and is rated at 35 mph. free-body diagram for the car is shown at left. When a road engineer designs the bend in a road they can make it safer by making it banked. Now, since the net force provides the centripetal A curved roadway has a radius of curvature of 200 meters and a bank angle of 10 If the coefficient of static friction for car tires on the road surface is 0.2, what is the highest speed at which a car can round the curve safely? Uniform Circular Motion - Velocity and Centripetal Force Vectors - Center Seeking Force2. In order to go in a circle, you know that you need an inward acceleration equal to v2/r. Our mission is to improve educational access and learning for everyone. An old streetcar goes around a corner on unbanked tracks. This force can supply a blue in the diagram above. A We can use the free-body diagram and derivation from example (e) The opposite direction of rotation is produced by the Coriolis force in the Southern Hemisphere, leading to tropical cyclones. banked curve even if the road is covered with perfectly smooth In this problem, a car is traveling in a circle on a banked incline. Looking at the OP, the correct solution is there ##v_{max} = \sqrt{gR ~tan( \theta + \theta_s)}## with ##\theta_s = arctan(\mu_s)##. (a) Calculate the ideal speed to take a 100 m radius curve banked at 15.0. Force of Gravity - Moon \u0026 Earth Example - Tangential Velocity3. But the force you exert acts toward the center of the circle. A minimum coefficient of friction is needed, or the car will move in a larger-radius curve and leave the roadway. A The easiest way to know where to put the 7.1o angles on your FBD is look at the small and large angles on your drawing. Each exhibits inertial forcesforces that merely seem to arise from motion, because the observers frame of reference is accelerating or rotating. Explore how circular motion relates to the bugs xy-position, velocity, and acceleration using vectors or graphs. If it is greater, friction is needed to provide centripetal force. If friction is present, therefore, it will act to prevent the tires from sliding out. As an amazon associate, I earn from qualifying purchases that you may make through such affiliate links. (It is of course true that most real curves are not exactly circles and so the rated speed isnt exactly the same throughout, unless the degree to which the road is banked also changes.). Talladega Motor Speedway in Alabama has turns with radius 1,100 One approach that always works is to solve one equation for one of the variables and substitute it into the other. Revolutions, Time in Seconds, Frequency, and Period9. The purpose of a banked curve is to provide an additional force, known as the centrifugal force, that helps keep vehicles on the road or track while turning. we can cross-multiply and solve for mu: Is this correct? Solve a Banked curve physics Problem - YouTube 0:00 / 7:24 Solve a Banked curve physics Problem 4,063 views Apr 2, 2017 We determine the rated speed for a banked turn of a given radius and. This car on level ground is moving away and turning to the left. This derivation is very The curve has a radius r. What is the speed v at which the car can turn safely? Viewed from above the North Pole, Earth rotates counterclockwise, as does the merry-go-round in Figure 6.27. So, lets see what the banking angle is and why it is so important. Conversely, wind circulation around high-pressure zones is clockwise in the Southern Hemisphere but is less visible because high pressure is associated with sinking air, producing clear skies. Continuing the derivation above, we can get: First, note that if the coefficient of friction were zero, the To find the value of the bank angle, we resort to the freebody diagram and proceed as follows. What does it mean that the banked curve is rated at a given speed? Why didnt you pick the x-axis to be along the incline? This physics video tutorial explains the concept of centripetal force and acceleration in uniform circular motion. Ultimately, the particles come into contact with the test tube walls, which then supply the centripetal force needed to make them move in a circle of constant radius. We analyze the forces in the same way we treat the case of the car rounding a banked curve. have been resolved into horizontal and vertical components. The cos component of normal force acts in the positive y direction. Likewise, the x-component is opposite to the 7.1o angle and is therefore given by n sin (7.1o). This video also covers the law of universal gravitation, weightlessness, banked curves with friction, kepler's third law of planetary motion and other stuff. stream Note that in this problem a small difference in truncation makes a very large difference in the answer, so as long as you approached the problem correctly dont worry too much about the numbers. How to calculate the distance between mercury and the sun32. As you can see in the figure, the x- and y-components of a vector make up the sides of a right triangle. Let's consider some examples. The banking angle shown in Figure 6.23 is given by . (b) In an inertial frame of reference and according to Newtons laws, it is his inertia that carries him off (the unshaded rider has. The curve is banked at angle with the horizontal, and is a frictionless surface. A car of mass m is turning on a banked curve of angle with respect to the horizontal. Each area represents a part of the universe that physicists have . For an object of mass m to execute uniform circular motion with speed v and radius r, it must be subjected to a net force that. (a) Calculate the ideal speed to take a 100.0 m radius curve banked at 15.0 15.0 . Force of Gravity Between Earth and the Sun24. A jet fighter is also flying around the airport with a speed of 800 km/h along a circular path with a radius of 2 km. Both the normal (Velocity and Acceleration of a Tennis Ball), Finding downward force on immersed object. Although most paths are not circular, most paths have parts that are approximately circular. The side of the triangle opposite the angle that you use is given by h sin and the side that touches the angle you use is given by h cos (soh cah toa) On the other hand, if the car is on a banked turn, the normal Even if no forces were mentioned, and you were asked, for example, for the degree to which the curve is banked, you know that it takes a net inward force to make an object move in a circle and so forces are the appropriate interactions to consider. fr cos(7.1o) + n sin(7.1o) = 1360 N But the wear and tear of tires caused by this friction increases the maintenance cost of the vehicles and increases the risk of sudden accidents at the curved points of the roads. The only two external forces acting on the car are its weight ww and the normal force of the road N.N. Note: Your initial thought might have been to resolve the This simplified model of a carousel demonstrates this force. [4.- mat/ . Friction is the only unknown quantity that was requested in this problem. The velocity of the car is directed into the page and is constant in magnitude. Tension Force on Rope attached to Ball - Horizontal Circle - Centripetal Force13. Unless both these conditions are true, the particle is not traveling with uniform circular motion. The vector itself forms the hypotenuse (h). Benefits of Banked curves and Banking angle: The banking angle at the curved turns of the roads (or Banked curves) reduces friction between the tires and the road and this, in turn, reduces maintenance costs and accidents of the vehicles.if(typeof ez_ad_units != 'undefined'){ez_ad_units.push([[320,50],'physicsteacher_in-box-4','ezslot_1',148,'0','0'])};__ez_fad_position('div-gpt-ad-physicsteacher_in-box-4-0'); Figure (a) shows a car going around a friction-free banked curve. Noting that tan 31.0 = 0.609, we obtain 1 ) Equation 3 indicates that, for a given speed v, the centripetal force needed for a turn of radius r can be obtained from the normal force FN by banking the turn at an angle . Solution Starting with tan = v 2 r g, we get v = r g tan . The side of the triangle opposite the angle that you use is given by h sin and the side that touches the angle you use is given by h cos (soh cah toa) The normal force not only balances against gravity (as seen in the y-equation) but also pushes the car inward around the circle (as seen in the x-equation.) In an "ideally banked curve," the angle is such that you can negotiate the curve at a certain speed without the aid of friction . Because this is the crucial force and it is horizontal, we use a coordinate system with vertical and horizontal axes. again that if mu = 0, this result reduces to the same Fnet as the The greater the angular velocity, the greater the centrifugal force. An object undergoing circular motion, like one of the race cars shown at the beginning of this chapter, must be accelerating because it is changing the direction of its velocity. b. JavaScript is disabled. That's a pretty extreme angle, even for a race track (see example Email:[emailprotected], Spotlight: Archives of American Mathematics, Policy for Establishing Endowments and Funds, National Research Experience for Undergraduates Program (NREUP), Previous PIC Math Workshops on Data Science, Guidelines for Local Arrangement Chair and/or Committee, Statement on Federal Tax ID and 501(c)3 Status, Guidelines for the Section Secretary and Treasurer, Legal & Liability Support for Section Officers, Regulations Governing the Association's Award of The Chauvenet Prize, Selden Award Eligibility and Guidelines for Nomination, AMS-MAA-SIAM Gerald and Judith Porter Public Lecture, Putnam Competition Individual and Team Winners, D. E. Shaw Group AMC 8 Awards & Certificates, Maryam Mirzakhani AMC 10 A Awards & Certificates, Jane Street AMC 12 A Awards & Certificates, Mathematics 2023: Your Daily Epsilon of Math 12-Month Wall Calendar. If additional information is needed, it will become apparent as you proceed. Notice that I've kept an extra 3 0 obj of friction is not zero, notice that the normal force will be larger Force and motion of a single object are always related through Newtons Second Law, so this is a force or 2nd Law problem. Air flows toward any region of low pressure, and tropical cyclones contain particularly low pressures. Given just the right speed, a car could safely negotiate a F: (240) 396-5647 From Figure 6.22, we see that the vertical component of the normal force is Ncos,Ncos, and the only other vertical force is the cars weight. A bug lands on a windshield wiper. When a car travels without skidding around an unbanked curve, the static frictional force between the tires and the road provides the centripetal force. By substituting the expressions for centripetal acceleration acac(ac=v2r;ac=r2),(ac=v2r;ac=r2), we get two expressions for the centripetal force FcFc in terms of mass, velocity, angular velocity, and radius of curvature: You may use whichever expression for centripetal force is more convenient. There is! The two legs of the triangle would be (163-111) on the bottom and 18 going up. xXKo7&.ho{I 5@X-Y#=M ?}P$ggWf~cIz|*=|rB!Krv#|zwV3T^lAbslllG=g]|70e' _Ab/.krpI U}q|tLsH#==;>DLp) hD ]t}@M&m=:@Yi3IXc2# BXq!LG]QJ@E`XSZlRZ[I&[Md*rN^j8$nlp;_#RyJFY9+8p^\8ee}#[[el/X[]v0w9kA :o\i 5p]A{Wt:.`wn>.\ a 2J7+lhOr&ow 3w{7M9gFhc# e1q+[g[1x %:?8$.S\G|#GFt*"$[s ' pDgp/y@90X6p'Ix8pfDxBtEmjCQJj.rz0cJOQc;BNydz].^W= pDQa0[E6i#p/P HE; (a) the normal force exerted by the pavement on the tires (b) the frictional force exerted by the pavement on the tires All you have to do is reverse the sign of ##\mu_s## in the formula you already have and replot. For uniform circular motion, the acceleration is the centripetal acceleration:.a=ac.a=ac. Read more here. The greater the angle , the faster you can take the curve. JavaScript is disabled. The audio is still there. Gravity acts straight down, friction acts down along the incline, and normal force acts out from the incline. An examination of the forces involved in this case are explained in this digital video. Solution: radius of curve, r = 50 m banking angle, = 15o free-fall acceleration, g = 9.8 m/s2 no friction speed, v = ? Larry Gladney is Associate Professor of Physics and Dennis DeTurck is Professor of Mathematics, both at the University of Pennsylvania. that there are now 3 vectors in the vertical direction (there were 2 The math is always easier if you pick one axis along the direction of acceleration. But what really happens is that the inertia of the particles carries them along a line tangent to the circle while the test tube is forced in a circular path by a centripetal force. Airplanes must also execute banked turns, since the air does not provide nearly enough friction to turn a massive plane moving a high speed. Only two significant figures were given in the text of the problem, so only two significant figures are included in the solution. Note that if you solve the first expression for r, you get. Because the car does not leave the surface of the road, the net vertical force must be zero, meaning that the vertical components of the two external forces must be equal in magnitude and opposite in direction. Acceleration is the effect of those forces and therefore does not show up on the FBD. A car of mass \(\displaystyle m\) is turning on a banked curve of angle \(\displaystyle \phi\) with respect to the horizontal. There is no problem to a physicist in including inertial forces and Newtons second law, as usual, if that is more convenient, for example, on a merry-go-round or on a rotating planet. If the coefficient The car is a noninertial frame of reference because it is accelerated to the side. The larger the. If the car has a speed of about 11 m/s, it can negotiate the curve If the angle is ideal for the speed and radius, then the net external force equals the necessary centripetal force. Car Rounding Curve - Static Friction Between Road \u0026 Tires and Centripetal Force4. Freely sharing knowledge with learners and educators around the world. What is the radius of the circular path the plane is flying? Banked curves in roads and racetracks are tilted inward (i.e. In this case, the car is traveling too fast for the curve. This inertial force is said to be an inertial force because it does not have a physical origin, such as gravity. significant digit in the result, though, just for safety's sake.) chapter 9 solutions glencoe physics principles problems web chapter ch9 problem 1cp step by step solution step 1 . To complete the graph, you might wish to consider a fourth color to separate the green region. radius = 56.4m mass_of_car = 2.3kg angle = 34 What I don't understand about this problem is why we assume there is only the normal force and the gravitational force on the vehicle. Textbook content produced by OpenStax is licensed under a Creative Commons Attribution License . have been resolved into horizontal and vertical components. According to Newtons second law of motion, net force is mass times acceleration: Fnet=ma.Fnet=ma. Whichever way you best understand friction in this case, you can see that is must be directed inward along the incline in order to help pull the car inward around the curve and to oppose sliding outward. <> Viewed from the rotating frame of reference, the inertial force throws particles outward, hastening their sedimentation. PROBLEM: A circular curve is banked so that a car traveling with uniform speed rouding the curve usualy relys on friction to keep it from slipping to its left or right. So to the number of significant figures included in this problem, we do not need to take buoyant force into account. horizontal direction. Likewise, the y-component is opposite to the 7.1o angle and is therefore given by fr sin (7.1o). and a bank angle of 15o (See the Example For a road or railroad this is usually due to the roadbed having a transverse down-slope towards the inside of the curve. surface) for a car on this curve? A physicist will choose whatever reference frame is most convenient for the situation being analyzed. what is desired to happen, in this case the car not slipping, cannot happen. Gravitational Acceleration 4000 Km above Earth's Surface27. you can make a triangle out of the info given. Learn More The image shows the many branches or areas of physics. In order to go in a circle, you know that you need an inward acceleration equal to v2/r. The car, as well as the driver, is actually accelerating to the right. Therefore, acceleration and the x-components of normal force and friction are all to the left and so are all negative. How To Solve a banked curve problem without friction PhysicsHigh 83.2K subscribers Subscribe Share 3.4K views 2 years ago problem solving This looks at a sample question involving. You could show both of those forces (which would be in the z-direction, or along the road) and that they cancel to zero if you like. derived for the no-friction case. Airplanes also make turns by banking. Inward Centripetal Force \u0026 Acceleration Vectors8. These two forces must add to give a net external force that is horizontal toward the center of curvature and has magnitude mv2/r.mv2/r. The latest Virtual Special Issue is LIVE Now until September 2023. is always directed centripetally, i.e. The FBD is now a visual representation of F=ma in each direction. the case, what coefficient of friction exists between the car's tires 20012023 Massachusetts Institute of Technology, Lesson 1: 1D Kinematics - Position and Velocity [1.1-1.7], Lesson 2: 1D Kinematics - Acceleration [2.1-2.5], Lesson 4: Newton's Laws of Motion [4.1-4.4], Lesson 8: Circular Motion - Position and Velocity [8.1-8.3], Lesson 9: Uniform Circular Motion [9.1-9.3], Lesson 10: Circular Motion Acceleration [10.1-10.4], Lesson 11: Newton's 2nd Law and Circular Motion [11.1-11.3], Week 4: Drag Forces, Constraints and Continuous Systems, Lesson 12: Pulleys and Constraints [12.1-12.5], Lesson 15: Momentum and Impulse [15.1-15.5], Lesson 16: Conservation of Momentum [16.1-16.2], Lesson 17: Center of Mass and Motion [17.1-17.7], Lesson 18: Relative Velocity and Recoil [18.1-18.4], Lesson 19: Continuous Mass Transfer [19.1-19.7], Lesson 20: Kinetic Energy and Work in 1D [20.1-20.6], Lesson 21: Kinetic Energy and Work in 2D and 3D [21.1-21.6], Lesson 22: Conservative and Non-Conservative Forces [22.1-22.5], Week 8: Potential Energy and Energy Conservation, Lesson 24: Conservation of Energy [24.1-24.4], Lesson 25: Potential Energy Diagrams [25.1-25.3], Lesson 26: Types of Collision [26.1-26.3], Lesson 27: Elastic Collisions [27.1-27.6], Deep Dive: Center of Mass Reference Frame [DD.2.1-DD.2.7], Lesson 28: Motion of a Rigid Body [28.1-28.3], Lesson 31: Rotational Dynamics [31.1-31.7], Lesson 32: Angular Momentum of a Point Particle [32.1-32.4], Lesson 33: Angular Momentum of a Rigid Body [33.1-33.5], Lesson 34: Torque and Angular Impulse [34.1-34.5], Week 12: Rotations and Translation - Rolling, Lesson 35: Rolling Kinematics [35.1-35.5], Lesson 37: Rolling Kinetic Energy & Angular Momentum [37.1-37.4].

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