9The Total Kinetic Energy of a Rolling Object is the sum of the rotational and the translational kinetic energy.K = ½ ICM ω2 + ½ MvCM2
10NoteRolling is possible when there is friction between the surface and the rolling object.The frictional force provides the torque to rotate the object.
11Ex: Accelerated Rolling Motion Ki + Ui = Kf + U fMgh = ½ ICM ω2 + ½ MvCM2vcm = ωRThere is no frictional work. Why not?Does friction cause a displacement at its point of action?
12Ex: #52A bowling ball (on a horizontal surface) has a mass M, radius R, and a moment of inertia of (2/5)MR2 . If it starts from rest, how much work must be done on it to set it rolling without slipping at a linear speed v? Express the work in terms of M and v. Hint: use kinetic energy theorem. Ans: (7/10)Mv2
13Ex: #54A uniform solid disk and a uniform hoop are placed side by side at the top of an incline of height h. If they are released from rest and roll without slipping, which object reaches the bottom first? Verify your answer by calculating their speeds when they reach the bottom in terms of h. Use conservation of energyAns: The disk, vdisk =(4gh/3)1/2 , vring =(gh)1/2
14Physics C: Rotational Motion Sample Problem3/31/2017A solid sphere of mass M and radius R rolls from rest down a ramp of height h and angle . Use Conservation of Energy to find the linear acceleration and the speed at the bottom of the ramp.Use kinematics for acceleration because force is constant.Bertrand
15Physics C: Rotational Motion Sample Problem3/31/2017A solid sphere of mass M and radius R rolls from rest down a ramp of length L and angle q. Use Rotational Dynamics to find the linear acceleration and the speed at the bottom of the ramp.Bertrand