A wheel of moment of inertia I and radius R is rotating about its axis at an angular speed `omega`. It picks up a stationary particle of mass `m` at its edge. Find the new angular speed of the wheel.

Explanation

Net external torque on the system is zero. Therefore, angular momentum will remain conserved. Thus,
`I_(1)omega_(1)=I_(2)omega_(2) or omega_(2)=(I_(1)omega_(1))/(I_(2))`
Here, `I_(1)=I,omega_(1)=omega_(0),I_(2)=I+mR^(2)`
`:. omega_(2)=(Iomega_(0))/(I+mR^(2))`.