A disc of moment of inertia I1 is rotating freely with...

A disc of moment of inertia $I_{1}$ is rotating freely with angular velocity $\omega_{1}$ when a second, non-rotating disc with moment of inertia $I_{2}$ is dropped on it gently the two then rotate as a unit. Then the total angular speed is (a) $\frac{I_{1} \omega_{1}}{I_{2}}$ (b) $\frac{I_{2} \omega_{1}}{I_{1}}$ (c) $\frac{I_{1} \omega_{1}}{I_{2}+I_{1}}$ (d) $\frac{\left(I_{1}+I_{2}\right) \omega_{1}}{I_{2}}$

A disc of moment of inertia $I_{1}$ is rotating freely with angular velocity $\omega_{1}$ when a second, non-rotating disc with moment of inertia $I_{2}$ is dropped on it gently the two then rotate as a unit. Then the total angular speed is
(a) $\frac{I_{1} \omega_{1}}{I_{2}}$
(b) $\frac{I_{2} \omega_{1}}{I_{1}}$
(c) $\frac{I_{1} \omega_{1}}{I_{2}+I_{1}}$
(d) $\frac{\left(I_{1}+I_{2}\right) \omega_{1}}{I_{2}}$

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Key Concepts

Angular Momentum Conservation

Angular momentum conservation states that in the absence of external torques, the total angular momentum of a system remains constant. In rotational collisions where the objects stick together, the sum of the individual angular momenta before the collision equals the total angular momentum of the combined system after the collision.

Moment of Inertia

The moment of inertia measures how an object's mass is distributed with respect to the axis of rotation, and it determines the resistance of the object to changes in its rotation rate. When two discs combine, their moments of inertia add, which affects the final rotational speed of the composite system.

Rotational Inelastic Collision

A rotational inelastic collision occurs when two rotating objects come into contact and coalesce, moving together with a common angular velocity afterward. In such collisions, while angular momentum is conserved, kinetic energy is not, making it necessary to use the conservation of angular momentum to determine the final angular speed.

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