Question

A pet mouse sleeps near the eastern edge of a stationary, horizontal turntable that is supported by a frictionless, vertical axle through its center. The mouse wakes up and starts to walk north on the turntable. (i) As it takes its first steps, what is the direction of the mouse’s displacement relative to the stationary ground below? (a) north (b) south (c) no displacement. (ii) In this process, the spot on the turntable where the mouse had been snoozing undergoes a displacement in what direction relative to the ground below? (a) north (b) south (c) no displacement. Answer yes or no for the following questions. (iii) In this process, is the mechanical energy of the mouse–turntable system constant? (iv) Is the momentum of the system constant? (v) Is the angular momentum of the system constant?

Short answer

(i) The answer is option (a) North

(ii) The spot on the turntable where the mouse had been snoozing undergoes a displacement in south direction relative to the ground below.

(iii) Mechanical energy is not conserved.

(iv) No

(v) Angular momentum is conserved.

Step-by-step solution

The direction of the mouse’s displacement relative to the stationary ground below

(i)

As the turntable has no velocity initially, the mouse first step is to the north. Hence, the answer is option (a).

Direction of the snoozing mouse relative to the ground below

(ii)

Due to the conservation of angular momentum, the turn table will spin in the clockwise direction that is it would spin under the mouse in the opposite direction.

Hence, the spot where the mouse slept will start moving towards south.

Therefore, option (b) is the right answer.

Mechanical energy

(iii)

No, as there is no kinetic energy in the system, the mouse uses its muscles to produce mechanical energy from the stored chemical energy.

Hence, the mechanical energy is not conserved.

Momentum

(iv)

No, the mouse is able to give itself linear momentum starting from rest as the fixed axle in the table is able to produce reactive forces.

Angular momentum

(v)

Yes, the axle in the table has no friction.

As it is frictionless, there is nothing capable of imparting any external torque to the system.

Hence, angular momentum is conserved.