Bob rolls a hollow sphere with a mass M = 6.82 kg and radius R = 10.9 cm up a hillside, giving it an initial kinetic energy of Ki.  It rolls over the top of the hill of height h and keeps going.  The ball rolls without slipping the whole way, but it loses Wnc due to non-conservative forces between the foot of the hill and the top. a.  Find its rotational inertia. b.  Given the height of the hill is h = 1.6 m, and Ki = 135 J, find the total kinetic energy Ktot at the top of the hill.

A solid 0.6350 kg ball rolls without slipping down a track toward a vertical loop of radius ?=0.6350 m. What minimum translational speed ?min must the ball have when it is a height ?=0.9944 m above the bottom of the loop in order to complete the loop without falling off the track? Assume that the radius of the ball itself is much smaller than the loop radius ?. Use ?=9.810 m/s^2 for the acceleration due to gravity.

1. A circular object of radius R starts from rest and rolls down an incline of M, I height H without slipping. The object has a mass M, a moment of inertia / and a radius R. We go through the steps in finding the speed of the object at the bottom of the incline below, a. What is the total mechanical energy of the object at the top of the incline? Write your answer in terms of I, M, R, H and/or g. b. What is the total mechanical energy at the bottom of the incline in terms of the speed v and the givens? Use the relation v = wR to eliminate the angular speed from your expression. Check that your expression has the correct dimensions. Your final expression should only contain v, I, M, R and/or g. When an object rolls without slipping, the point in contact with the ground is at rest. Therefore, the friction the mechanical energy C. force has displacer work, conserved. Use conservation of mechanical energy to find the speed v of the object at the bottom of the hill in terms of I, R, M,H…

T m A 25.0 kg mass is hung from a rope that is passed over a pulley and held by a man standing on a ramp. The pulley can be treated as a solid disk with a mass of 10.0 kg that has a radius of 0.400 m. The man pulls the rope so that the pulley rotates from rest through an angular displacement of 15.0 rad in 2.00s. A. What is the angular acceleration of the disk? B. What is the tension of the rope as it pulls up on the box? C. What is the force applied by the man on the rope as he pulls the box upward?

3 1. A uniform solid sphere rolls without slipping down a 28° inclined plane. What is the acceleration of the sphere's center of mass? The moment of inertia of a uniform solid sphere about an axis that passes through its center = mr². The moment of inertia of a uniform solid sphere about an axis that is tangent to its surface = 7/5mr². m/s² E D C 4 22 R F % 5 V T G tv B MacBook Air 22 Y H 7 5 N 00 8 ZA 3 ( 9 K MOSISO O O V P command DUI 04 M option

A 6 cm diameter, 550 g solid sphere is released from rest at the top of a 2.0 m long, 35° incline. It rolls, without slipping, to the bottom. a. What is the sphere’s angular velocity at the bottom of the incline?b. What fraction of its kinetic energy is rotational?

A hollow sphere with a radius R and a mass M (note that I = (2/3)MR^2 for a hollow sphere) rolls down an incline with an angle θ. Its acceleration down the ramp is given by: A. 5/3gsinθ B. gsinθ  C. 3/5gsinθ D. 1/2gsinθ A solid uniform disk with a radius R and a mass M (note that I = (1/2)MR^2 for a solid disk) rolls down an incline with an angle θ. Its acceleration down the ramp is given by: ⃝ A. 5/3gsinθ ⃝ B. gsinθ  ⃝ C. 2/3gsinθ  ⃝ D. 1/2gsinθ