Question

The moment of inertia, /, of an object traveling in a circular path is

given by the equation /=mr²2, where m is the mass and ris the
radius of the circular path. If the radius of the path is increased by 30%
while the mass is held constant, how does the moment of inertia
change?

Answer 1

The new radius will be 1.3 times the original radius, so r_new = 1.3r_old. Plugging this into the equation for moment of inertia, we get:

I_new = m * r_new^2 / 2

= m * (1.3r_old)^2 / 2

= m * 1.69 * r_old^2 / 2

= 1.69 * (m * r_old^2 / 2)

= 1.69 * I_old

Therefore, the moment of inertia increases by 69% when the radius is increased by 30% while the mass is held constant.