Question

A gyroscope slows from an initial rate of 34 rad/s at a rate of 0.619 rad/s2. The angular displacement when it stops moving is _

Answer 1

Answer: $933.76\ rad$

Explanation:

Given

The initial rate of gyroscope is $\omega_o=34\ rad/s$

Angular deceleration $\alpha =0.619\ rad/s^2$

Using angular equation of motion

$\Rightarrow \omega^2-\omega_o^2=2\alpha \theta$

Insert the values

$\Rightarrow 0-34^2=2(-0.619)\theta \\\\\Rightarrow \theta =\dfrac{34^2}{2\times 0.619}\\\\\Rightarrow \theta =933.76\ rad$

Thus, the angular displacement is $933.76\ rad$