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

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

Step-by-step explanation:

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

`I = (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 = (1)/(2)mr^2\\ \\I_2 = (1)/(2)(7m)(15r)^2\\\\I_2 = (1)/(2)(7m)(225r^2)\\\\I_2 = 7* 225[(1)/(2)(mr^2)]\\\\I_2 = 1575[(1)/(2)(mr^2)]\\\\Recall, (1)/(2)(mr^2) = I_1 \\\\I_2 = 1575 I_1`

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