Three rigid systems—P, Q, and R—rotate about fixed, frictionless vertical axes through their centers. The net external torques and rotational inertias for the systems are listed in the table below.
System
Net External Torque (about axis)
Rotational Inertia
P
2τ0
I0
Q
τ0
2I0
R
3τ0
3I0
Here τ0 and I0 are positive constants with appropriate units.
(a) Rank the magnitudes of the angular accelerations of systems P, Q, and R from largest to smallest. Clearly justify the reasoning that leads to your ranking.
(b) Suppose a fourth system S has the same rotational inertia as system P but experiences a net external torque of 4τ0. Compare the angular acceleration of system S with that of system P, explaining the physical basis for any difference.
(c) System Q is modified by redistributing some of its mass so that its rotational inertia is halved while the applied torque remains τ0. Describe quantitatively how its angular acceleration changes and explain why.
(d) A student claims that doubling both the net external torque and the rotational inertia of any system must leave its angular acceleration unchanged. Evaluate this claim using one of the systems above as an example, and provide a clear argument supporting your evaluation.