Question

wo ladybugs of the same mass are on a record that is on a record player. The record player is turned on and it reaches a constant velocity. show answer No Attempt If the male ladybug is all the way at the edge and the female ladybug is halfway between the center and the edge, what can be said about their moments of inertia?

Answer 1

Answer:

The moment of inertia of the male ladybug is 4 times the moment of inertia of the female ladybug.

Explanation:

The moment of inertia of a single-point object rotating about an axis is given by

$I=mr^2$

where

m is the mass of the object

r is the distance of the object from the axis of rotation

In this problem, we have:

- The mass of the two ladybugs is the same, $m_M=m_F$

- The distance of the male ladybug from the axis of rotation is twice that of the female ladybug, $r_M=2r_F$

So, the moment of inertia of the female ladybug is

$I_F=m_F r_F^2$

While the moment of inertia of the male ladybug is

$I_M = m_M r_M^2 = m_F (2r_F)^2=4 m_F r_F^2=4I_F$

Therefore, the moment of inertia of the male ladybug is 4 times the moment of inertia of the female ladybug.