A thin hoop and a solid disk have the same mass and radius
PHYSICS · Single correct · AP · Physics 1: Algebra-based · Torque and Rotational Dynamics · Torque and Rotational Dynamics
Problem
A thin hoop and a solid disk have the same mass M and radius R. Both rotate about an axis through their centers and perpendicular to their planes. Which of the following best explains why the hoop has the greater rotational inertia?
(a) Because every part of the hoop travels at the rim’s linear speed v=ωR, its rotational kinetic energy is higher than that of the disk at the same angular speed; therefore its rotational inertia must be larger.
(b) The hoop encloses more empty space than the disk, so its total mass must resist rotation more strongly.
(c) A larger fraction of the hoop’s mass is located at distance R from the axis, so mr2 is larger for each mass element.
(d) The hoop has a larger ratio R3/M, and using the relation I=21MR3 gives it the greater rotational inertia.