Question

A mouse of mass m jumps on the outside edge of a rotating ceiling fan of the moment of inertia l and radius R. The frictionless loss of angular velocity of the fan as a result is, 

• A. \(\frac{mR^2}{1+mR^2}\)
• B. \(\frac{1}{1+mR^2}\)
• C. \(\frac{1-mR^2}{1}\)
• D. \(\frac{1-mR^2}{1+mR^2}\)

Answer 1

The Correct Option is A

As we know from Newton's first law of motion, an object in motion will retain its state of motion (velocity to be precise) unless an external force is applied on the object. We can use the same sense of the law in rotation, i.e. to the state of rotational motion, or precisely, rotational velocity. However, since it is rotational motion we are talking about, we have to always keep in mind the momentary position vector of any particle constituting the rotational motion. If we take into account all the momentary position vectors, they will constitute a disc of which the axis is along Z axis.

Now, for a particle in linear motion, a force along the direction of velocity cannot change the direction of velocity. In the same analogy, any force along the direction of the axis of the disc cannot change the direction of the axis of the disc. Only a force that has a component perpendicular to the Z axis will change the direction of the axis of the disc, thus changing the plane of rotation.

The correct answer is option (A): \(\frac{mR^2}{1+mR^2}\)