Question

A hollow cylinder (hoop) of mass M and radius R starts rolling without slipping (with negligible initial speed) from the top of an inclined plane with angle theta. The cylinder is initially at a height h from the bottom of the inclined plane. The coefficient of friction is u. The moment of inertia of the hoop for the rolling motion described is I= mR^2.

a) What is the magnitude of the net force and net torque acting on the hoop? Derive expressions for the angular and linear acceleration of the hoop.

b) Using the principle of conservation of energy, derive an expression for the speed of the hoop at the bottom of the incline.

c) Using the results from part a) derive an expression for the speed of the hoop at the bottom of the incline. Show that this result agrees with the speed you obtain using the conservation of energy.

Answer #1

Problem 4
A hoop and a solid disk both with Mass (M=0.5 kg) and radius (R=
0.5 m) are placed at the top of an incline at height (h= 10.0 m).
The objects are released from rest and rolls down without
slipping.
a) The solid disk reaches to the bottom of the inclined plane
before the hoop. explain why?
b) Calculate the rotational inertia (moment of inertia) for the
hoop.
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A solid cylinder starts rolling without slipping from the top of
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