Fundamentals of Physics 10e. Chapter 11 Problem 50. See below. The Chegg solutio

Question

Fundamentals of Physics 10e. Chapter 11 Problem 50. See below. The Chegg solution says that due to Conservation of Angular Momentum that the angular momemtum of the motor (Lm) equals the angular momemetum of the probe (Lp). Given the definition of Conservation of Angular Momentum is "L initial = L final" I am have having trouble understanding why the solution assumes Lm=Lp..   Can you please explain why Lm=Lp in the context of L initial = L final? I understand the rest of the solution.

50P. The rotor of an electric motor has rotational inertia Im = 2.0 x 10^-3 kg m2 about is central axis. The motor is used to change the orientation of the space probe in which it is mounted. The motor axis is mounted along the central axis of the probe; the probe has rotational inertia Ip = 12 kg m2 about this axis. Calculate the number of revolutions of the rotor required to turn the probe 30 degrees about its central axis..

Explanation / Answer

Hello,

First of all, Let's understan the angular momentum with respect to rigid bodies.

L = I*w where w = omega

Now, As given in the question, moment of inertia for motor and probe is different. We must understand that moment of inertia is resistance to angular acceleration. If we look at the question, the motor axis of rotation lies along or we can say coincides with the space probe's axis of rotation. So, the angular velocity part will be very much same. We can say that to conserve the momentum the probe and motor have same angular velocity and as they have common axis of rotation, the moment of inertia balances out.

It gives us that angular momentum of motor equal to angular momentum of probe.

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