A rotating body's kinetic energy K relies on its moment of inertia I and its angular speed ω . Suppose the relation is K = kI^a ω^b , where k is a dimensionless constant. Determine a and b . The moment of inertia of a

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Correct answer: C. a = 1, b = 2

Using dimensional analysis, the dimensions of the given quantities are:

[K] = [M L^2 T^{-2}]

[I] = [M L^2]

[\omega] = [T^{-1}]

Substituting these into the given relation

K = k I^a \omega^b

:

[M L^2 T^{-2}] = [M L^2]^a [T^{-1}]^b

[M L^2 T^{-2}] = [M^a L^{2a} T^{-b}]

Comparing the powers of

M

,

L

, and

T

on both sides:

For

M

:

a = 1

For

T

:

-b = -2 \Rightarrow b = 2

Therefore,

a = 1

and

b = 2

.

A rotating body's kinetic energy K relies on its moment of inertia...

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