A child of mass m is standing at the edge of a carousel. Both the carousel and the child are initially stationary. The carousel is a large flat, uniform disc of mass M, and radius R, which turns on a frictionless pivot at its center. It has moment of inertia I = MR2 /2. The child is very small compared to the carousel. The child starts to run around the edge of the carousel at speed v. The direction of child is counter-clockwise when the carousel is viewed from above. Taking the z-axis as upwards, what is the angular velocity of the carousel after the child has started running?

the angular velocity of the carousel after the child has started running =

Explanation:

Given that

the mass of the child = m

The radius of the disc = R

moment of inertia I =

change in time =

By using the torque around the inertia ; we have:

T = I×∝

where

R×F = I × ∝

R×F = ∝

F = ∝

∝ =           ( expression for angular  angular acceleration)

The first equation of motion of rotating wheel can be expressed as :

where ;

∝ =    

Then;

∴ the angular velocity of the carousel after the child has started running =

answer: 2×10^-2kg

explanation: density= mass per volume

vol=mass/density

converting to s.i units we have;

3÷1000kg = 0.003

1.5÷100m = 0.15

0.003/0.15 = 0.02kg