The kinetic energy K of a rotating body depends on its moment of inertia I and its angular speed ω. Assuming the relation to be K = kI a ω b where k is a dimensionless constant, find a and b. Moment of inertia of a sphere about its diameter is Mr 2 .

Question

Philoid · Accepted Answer

K = k I^a ω^b

Dimensions of K = [ML²T^-2]

Dimensions of I = [ML²]

Dimensions of ω = [T^-1]

Dimensionally

[ML²T^-2] = [ML²] ^a [T^-1] ^b

= [ ML^2aT^-b]

From here 2a = 2 and -2 = -b

So a = 1 and b = 2.

The kinetic energy K of a rotating body depends on its momentof inertia I and its angular speed ω. Assuming the relation to be K =kIa ωb where k is a dimensionless constant, find a and b. Moment ofinertia of a sphere about its diameter is Mr2.

The kinetic energy K of a rotating body depends on its moment
of inertia I and its angular speed ω. Assuming the relation to be K =

kI^a ω^b where k is a dimensionless constant, find a and b. Moment of

inertia of a sphere about its diameter is Mr².