Chapter 10: Rotational Motional About a Fixed Axis

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Presentation transcript:

Chapter 10: Rotational Motional About a Fixed Axis Review of Angular Quantities & Motion and Torque (10-1,10-2,10-3, 10-5) Solving Problems in Rotational Dynamics (10-6, 10-7) Determining Moments of Inertia, Conservation of Angular Momentum, and Rotational Kinetic Energy (10-8,10-9, 10-10) Rotational + Translational Motion (10-11, 10-12) 11/7/2018 Physics 253

11/7/2018 Physics 253

Example 1: The Torque on a Braking Car. Interestingly enough when a car brakes the force on the front brakes exceed the force on the back brakes. This is related to the torque around the center of mass. Consider the car at right which has a mass of M=1200kg and is decelerating at 0.50g. 11/7/2018 Physics 253

11/7/2018 Physics 253

11/7/2018 Physics 253

11/7/2018 Physics 253

11/7/2018 Physics 253

The Line Integral for “Rotational” Work The work done on a rotating body about a fixed axis can written in terms of angular quantities. Suppose a force F is exerted at a distance from the axis of rotation as shown in the figure. 11/7/2018 Physics 253

11/7/2018 Physics 253

Rotational + Translational Motion An object in translation has kinetic energy which can be described by the total mass M and the velocity of the CM vCM: KE= (1/2)M vCM2 An object rotating about an axis through it’s center of mass has rotational kinetic energy given by KE= (1/2)ICM w2 An object such as a rolling wheel has both! KE= (1/2)M vCM2+(1/2)ICM w2 11/7/2018 Physics 253

Example 2: Rolling Sphere A solid sphere of mass M and radius R starts at rest and rolls down an incline of height H. Ignoring friction and assuming there is no slippage what’s the final velocity? 11/7/2018 Physics 253

11/7/2018 Physics 253

11/7/2018 Physics 253

Example 3: What about a Hoop or a Cylinder? 11/7/2018 Physics 253

11/7/2018 Physics 253

Proof of KE=(1/2)M vCM2+(1/2)ICM w2 The most general statement is: the total kinetic energy of a moving body will be equal to the translational kinetic energy of its CM plus the kinetic energy of the motion of the object relative to the center of mass. Starting with the figure at the right, this is really a vector argument. 11/7/2018 Physics 253

11/7/2018 Physics 253

11/7/2018 Physics 253

11/7/2018 Physics 253

Example 4: A Yo-yo’s Acceleration! Approximate the shape of a yo-yo as that of a solid cylinder of mass M and radius R. As it falls and unwinds the string find the acceleration and tension in the string. 11/7/2018 Physics 253

11/7/2018 Physics 253

Example 5: How Long Does It Take for a Slipping Ball to Roll? A bowling ball of mass and radius R is thrown down the alley. Initially it slides with linear speed vo. As it slides it begins to roll. How long before it is completely rolling with out slipping? 11/7/2018 Physics 253

11/7/2018 Physics 253

11/7/2018 Physics 253

In Chapter 11 we continue to explore angular momentum We Are in the Stretch! There are four lessons left involving Chapter 11 and a bit of Chapter 12. In Chapter 11 we continue to explore angular momentum In Chapter 12 we study equilibrium. The next Quiz is May 2. You know the drill by now! 11/7/2018 Physics 253