When a dancer pulls their arms inward while spinning on ice,they spin faster. This is due to:

$A$ person standing on a rotating table holds weights in their outstretched hands and is rotating. They suddenly pull their hands in close to their body. Which statement is true?

$A$ force $\vec F = \alpha \hat i + 3\hat j + 6\hat k$ is acting at a point $\vec r = 2\hat i - 6\hat j - 12\hat k$. The value of $\alpha$ for which angular momentum about the origin is conserved is:

$A$ horizontal disc rotating freely about a vertical axis through its centre makes $90$ revolutions per minute. $A$ small piece of wax of mass $m$ falls vertically on the disc and sticks to it at a distance $r$ from the axis. If the number of revolutions per minute reduces to $60$,then the moment of inertia of the disc is .........

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

$A$ thin uniform rod of mass $M$ and length $L$ is rotating about a perpendicular axis passing through its centre with a constant angular velocity $\omega$. Two objects,each of mass $\frac{M}{3}$,are attached gently to the two ends of the rod. The rod will now rotate with an angular velocity of