A solid sphere of mass

PHYSICS · Multi-part · AP · Physics 1: Algebra-based · Energy and Momentum of Rotating Systems · Energy and Momentum of Rotating Systems

Problem

A solid sphere

(k=\tfrac{2}{5})

of mass

0.50\,\text{kg}

, a thin hoop

(k=1)

of mass

0.50\,\text{kg}

, and a solid cylinder

(k=\tfrac{1}{2})

of mass

1.0\,\text{kg}

each have radius

0.10\,\text{m}

. They are released from rest at the top of a straight ramp of vertical height

2.0\,\text{m}

and length

4.0\,\text{m}

. The ramp is rough enough to prevent slipping, and air resistance is negligible. (a) Calculate the magnitude of the translational speed of the center of mass of each object at the bottom of the ramp. (b) Assuming the acceleration of each object remains constant along the ramp, determine the time taken by each object to reach the bottom. (c) Compare your answers for the hoop and the cylinder to discuss whether mass plays any role in determining the motion of rolling objects under these conditions.

Related theory

Browse the problem library