A record of mass M and radius R is free to rotate around an axis through its center, O. A tangential
force F is applied to the record. What must one do to maximize the angular acceleration?
(A)Make F and M as large as possible and R as small as possible
(B)Make M as large as possible and F and R as small as possible.
(C)Make F as large as possible and M and R as small as possible.
(D)Make R as large as possible and F and M as small as possible.
(E)Make F, M, and R as large as possible.To answer this question, you don’t need to know exactly what a disc’s moment of inertia is—you
just need to be familiar with the general principle that it will be some multiple of MR^2.
The rotational version of Newton’s Second Law tells us that = I , and so = FR/I. Suppose we
don’t know what I is, but we know that it is some multiple of MR^2. That’s enough to formulate an
equation telling us all we need to know:
As we can see, the angular acceleration increases with greater force, and with less mass and
radius; therefore C is the correct answer.
Alternately, you could have answered this question by physical intuition. You know that the more
force you exert on a record, the greater its acceleration. Additionally, if you exert a force on a
small, light record, it will accelerate faster than a large, massive record.
EXAMPLE 2