Equations of Rotational Motion Video Lessons

Concept

Problem: A gyroscope slows from an initial rate of 32.0 rad/s at a rate of 0.700 rad/s2.(a) How long does it take to come to rest?(b) How many revolutions does it make before stopping?

FREE Expert Solution

We'll use the equation:

$\overline{){{\mathbf{\omega }}}_{{\mathbf{f}}}{\mathbf{=}}{{\mathbf{\omega }}}_{{\mathbf{0}}}{\mathbf{+}}{\mathbf{\alpha }}{\mathbf{t}}}$

We'll also use the equation:

$\overline{){\mathbit{\theta }}{\mathbf{=}}{{\mathbf{\omega }}}_{{\mathbf{0}}}{\mathbf{t}}{\mathbf{+}}\frac{\mathbf{1}}{\mathbf{2}}{{\mathbf{\alpha t}}}^{{\mathbf{2}}}}$

(a)

Find t from the first equation as follows:

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Problem Details

A gyroscope slows from an initial rate of 32.0 rad/s at a rate of 0.700 rad/s2.

(a) How long does it take to come to rest?

(b) How many revolutions does it make before stopping?