A uniform thin hoop of mass and radius can be rotated about two different fixed axes
PHYSICS · Multi-part · CBSE · Physics · System of Particles and Rotational Motion · System of Particles and Rotational Motion
Problem
A uniform thin hoop of mass M and radius R can be rotated about two different fixed axes, each axis being perpendicular to the plane of the hoop:
• Axis C passes through the center of the hoop.
• Axis S is parallel to Axis C but intersects the plane of the hoop at a point on the hoop’s rim, a distance R from the center.
Assume the hoop is always rotated with its plane remaining horizontal.
(a) Without performing a numerical calculation, state which axis—C or S—gives the larger rotational inertia for the hoop. Provide a clear physical explanation based on the distribution of mass relative to each axis.
(b) Describe qualitatively, in words or with a sketch, how the rotational inertia of the hoop changes as the axis is moved continuously from Axis C to Axis S. Identify the feature of the system that controls the rate of change.
(c) Suppose the hoop is set spinning at the same angular speed ω about each axis separately. Compare the rotational kinetic energies KC and KS for the two cases. Explain your reasoning in terms of the results from parts (a) and (b).