Question

If the mass of a wheel is increased by a factor of 7 and the radius is increased by a factor of 15, by what factor is the moment of inertia increased

Answer 1

Answer:

The moment of inertia will be increased by a factor of 1575

Explanation:

Let the moment of inertia of a wheel be given as;

$I = \frac{1}{2} mr^2$

where;

I is the moment of inertia of the wheel

m is mass of the wheel

r is radius of the wheel

when the mass is increased by a factor of 7 and the radius is increased by a factor of 15

$I_1 = \frac{1}{2}mr^2\\ \\I_2 = \frac{1}{2}(7m)(15r)^2\\\\I_2 = \frac{1}{2}(7m)(225r^2)\\\\I_2 = 7\times 225[\frac{1}{2}(mr^2)]\\\\I_2 = 1575[\frac{1}{2}(mr^2)]\\\\Recall, \frac{1}{2}(mr^2) = I_1 \\\\I_2 = 1575 I_1$

Thus, the moment of inertia will be increased by a factor of 1575