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A wheel of moment of inertial I and radi...

A wheel of moment of inertial 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.

Text Solution

Verified by Experts

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) = (l_(1) omega _(1))/(l_(2))`
Here, `I_(1) = I, omega_(1) = omega _(0), I_(2) = I + mR^(2)`
`:. omega_(2) = (lomega_(0))/(l + mR ^(2))`
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Knowledge Check

  • A solid cylinder of mass M and radius R rotates about its axis with angular speed omega . Its rotational kinetic energy is

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