The mass of a hoop of radius 1.2 m is 6.7 kg. It rolls without slipping across a horizontal surface with a speed of 10.2 m/s. (a) How much work (in J) is required to stop the hoop? (b) If the hoop rolls without slipping up a surface at 40° to the horizontal with an initial speed of 10.2 m/s, how far along the incline will it travel (in m) before stopping and rolling back down?

A solid cylinder with a mass of (5 kg) and a radius of (0.2 m) (I =12MR2) is initially rolling along a flat plane with a linear velocity of (10ms). The cylinder then comes to the edge of a ramp that is inclined by (34degrees) to the horizontal and begins to roll up the ramp. How high above the flat plane does the cylinder reach before it starts to roll back down?

A hollow cylinder has radius 9.5 cm and mass 1.8 kg. The cylinder rolls without slipping at a speed of 1.488 m/s, and begins to roll without slipping up a(n) 11° slope. What is the maximum height the cylinder will reach on the inclined plane when it comes to a stop?

A thin cylindrical ring starts from rest at a height h1 = 98 m. The ring has a radius R = 34 cm and a mass M = 4 kg. Part (a)  Write an expression for the ring's initial energy at point 1, assuming that the gravitational potential energy at point 3 is zero.  Part (b)  If the ring rolls (without slipping) all the way to point 2, what is the ring's energy at point 2 in terms of h2 and v2?  Part (c)  Given h2 = 32 m, what is the velocity of the ring at point 2 in m/s? Part (d)  What is the ring's rotational velocity in rad/s? Part (e)  After passing point 2 the hill becomes frictionless and the ring's rotational velocity remains constant. What is the linear velocity of the ring at point 3 in m/s?

Problem 151. One end of a rod of mass 1 kg and of length 1 m can freely rotate about a lixed horizontal axis. Initially the rod makes an angle of 30° to the horizontal. A thread of length 1.3 m is attached t0 the (wo ends of the rod. A small pulley can run without friction along the thread, and a weight of mass 0.2 kg is suspended on the axis of the pulley. Determine the work needed to lit the rod to a horizontal position. (Use the value g= 10 m/s? for the acceleration due to gravity.) 30° 1 m

In the system , a 12.0 kg mass is released from rest and falls, causing the uniform 10.0 kg cylinder of diameter 30.0 cm to turn about a frictionless axle through its center. How far will the mass have to descend to give the cylinder 480 J of kinetic energy?