Q28DQ - University Physics with Modern Physics

Question

A gyroscope takes 3.8 s to precess 1.0 revolution about a vertical axis. Two minutes later, it takes only 1.9 s to precess 1.0 revolution. No one has touched the gyroscope. Explain.

Step-by-Step Solution

Answer

The spinning gyroscope has slowed down which doubled the precession angular speed.

Step 1: Given that

A gyroscope takes 3.8 s to precess 1.0 revolution about a vertical axis. Two minutes later, it takes only 1.9 s to process 1.0 revolution. No one has touched the gyroscope.

Step 2: Formula used

Precession angular speed is

$\Omega =\frac{wr}{lw}$ where,

w is weight of the flywheel

r is distance from the pivot

I is moment of intertia and

$\omega$ angular speed.

Step 3: Explanation

Over two minutes, friction causes angular speed $\omega$ of the spinning flywheel to decrease by a factor of 2, which doubles the precession angular speed.

So it takes half time to precess 1 revolution.