Kevin S. Huang

2007: Problem 10

Topic: Rigid Bodies
Concepts: Rotational Newton’s 2nd law

Solution:

Recall for rotational motion,

\tau=I\alpha

We are given the moment of inertia of the wheel:

I=mR^2

The force is applied perpendicular to the moment arm:

\tau=FR

Thus,

FR=mR^2\alpha

F=mR\alpha

Both wheels have the same mass, so for both to have the same angular acceleration,

F \propto R

Hence,

R_2=2R_1

F_2=2F_1=2 \,\mathrm{N}

so the answer is D.