Home
Class 12
PHYSICS
A disc is rotating with angular speed om...

A disc is rotating with angular speed `omega_(1)`. The combined moment of inertia of the disc and its axle is `I_(1)`. A second disc of moment of inertia `I_(2)` is dropped on to the first and ends up rotating with it. Find the angular velocity of the combination if the original angular velocity of the upper disc was (a) zero (b) `omega_(2)` in the same direction as `omega_(1)` and (c) `omega_(2)` in a direction opposite to `omega_(1)`.

Text Solution

Verified by Experts

The total angular momentum of the system before coupling `= |I_(1) vec(omega)_(1) + I_(2) vec(omega)_(2)|`
`{:(("The total angular momentum"),("after coupling when they rotate with"),("equal angular velocity")):}=|I_(1) vec(omega) + I_(2) vec(omega)|`
Conservation of angular momentum
`|(I_(1) + I_(2))vec(omega)| = |I_(1) vec(omega)_(1) + I_(2) vec(omega)_(2)| " "rArr" "omega = (|I_(1)vec(omega)_(1) + I_(2)vec(omega)_(2)|)/((I_(1) + I_(2)))`
(a) When `omega_(2) = 0, omega = (omega_(1))/((I_(2)//I_(1))+1)`
(b) When `omega_(1) and omega_(2)` are unidirectional, `omega = (I_(1) omega_(1) + I_(2) omega_(2))/((I_(1) + I_(2)))`
(c) When `omega_(1) and omega_(2)` are anti - parallel, `omega = (|I_(1) omega_(1) - I_(2) omega_(2)|)/(I_(1) + I_(2))`
Promotional Banner

Similar Questions

Explore conceptually related problems

A disc is rotating with angular velocity omega . If a child sits on it, what is conserved?

A disc with moment of inertia I is rotating with some angular speed. Second disc is initially at rest. Now second disc with moment of inertia 3I is placed on first disc and starts rotating. Find loss of kinetic energy in fraction

A disc with moment of inertial I is rotating with some angular speed. Second disc is initially at rest. Now second disc with moment of inertia 3I is placed on first disc and starts rotating. Find loss of kinetic energy in fraction

When a disc rotates with uniform angular velocity, which of the following is not true ?

When a disc rotates with uniform angular velocity, which of the following is not true ?

A round disc of moment of inertia I_2 about its axis perpendicular to its plane and passing through its centre is placed over another disc of moment of inertia I_1 rotating with an angular velocity omega about the same axis. The final angular velocity of the combination of discs is.

A cockroach is moving with velocity v in anticlockwise direction on the rim of a disc of radius R of mass m . The moment of inertia of the disc about the axis is I and it is rotating in clockwise direction with an angular velocity omega . If the cockroach stops, the angular velocity of the disc will be

An ant is sitting at the edge of a rotating disc. If the ant reaches the other end, after moving along the diameter, the angular velocity of the disc will:-

A disc of mass m and radius R rotating with angular speed omega_(0) is placed on a rough surface (co-officient of friction =mu ). Then

A uniformly charged disc of radius r and having charge q rotates with constant angular velocity omega . The magnetic dipole moment of this disc is (1)/(n)qomegar^(2) . Find the value of n.