Question

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

Answer 1

Answer:

$t=45.7s$

$\alpha =116revolutions$

Explanation:

Since we have given values of ω₀=32.o rad/s ,ω=0 and α=-0.700 rad/s² to find t we use below equation

$w=w_{o}+at\\ 0=(32.0rad/s)+(-0.700rad/s^{2} )t\\t=\frac{-32.0}{-0.700} \\t=45.7s$

To find revolutions we use below equation

$w^{2}=w_{o}^{2}+2a\alpha$

Substitute the given values to find revolutions α

So

$0=(32.0rad/s)^{2}+2(-0.700rad/s^{2} )\alpha \\\alpha =\frac{(-32.0rad/s)^{2}}{2(-0.700rad/s^{2} )} \\\alpha =731rad$

To convert rad to rev:

$\alpha =(731rad)*(\frac{1rev}{2\pi rad} )\\\alpha =116revolutions$