Which of the following best explains why a plot of rotational kinetic energy versus…

PHYSICS · Single correct · AP · Physics 1: Algebra-based · Energy and Momentum of Rotating Systems · Energy and Momentum of Rotating Systems

Problem

Which of the following best explains why a plot of rotational kinetic energy versus

\omega^2

for a single rigid object is expected to be linear? (a) Because

K_{\text{rot}}

depends linearly on

\omega

for a rigid body experiencing uniform angular acceleration. (b) Because conserving angular momentum requires

K_{\text{rot}}

to rise at a constant rate as

\omega^{2}

increases. (c) Because a rigid object has a constant moment of inertia

I

, and since

K_{\text{rot}}=\tfrac12 I\omega^{2}

K_{\text{rot}}

is directly proportional to

\omega^{2}

. (d) Because rotational kinetic energy is analogous to translational kinetic energy

\tfrac12 m v^{2}

, so replacing

v

with

\omega

gives

\tfrac12 m\omega^{2}

, which is linear in

\omega^{2}