A gyroscope slows from an initial rate of 49.3 rad/s at a rate of 0.731 rad/s^2. (a) How long does it take (in s) to come to rest? (b) How many revolutions does it make before stopping?

(a) 67.44 second

(b) 529.5 revolutions

Explanation:

ωo = 49.3 rad/s

α = 0.731 rad/s^2

(a) Let it takes t time to come to rest.

ω = 0

Use first equation of motion for rotational motion

ω = ωo + α t

0 = 49.3 - 0.731 x t

t = 67.44 second

(b) Let it turns an angle θ rad before coming to rest. use third equation of motion for rotational motion.

ω^2 = ωo^2 + 2 α θ

0 = 49.3 x 49.3 - 2 x 0.731 x θ

2430.49 = 1.462 θ

θ = 1662.44 rad

Number of revolutions = θ / 2π = 1662.44 / 3.14 = 529.5 revolutions