With the aid of a string, a gyroscope is accelerated from rest to 32 rad/s in 0.40 s. What is its angular acceleration in rad/s2

Question

2 years ago

11

? How many revolutions does it go through in the process?

1 answer:

Irina-Kira [14] · Answer 1 · 2022-08-01T00:12:13+03:00

<h2>Angular acceleration is 80 rad/s² </h2><h2>Number of revolutions undergone is 1.02</h2>

Explanation:

We have equation of motion v = u + at

Initial angular velocity, u = 0 rad/s

Final angular velocity, v = 32 rad/s

Time, t = 0.40 s

Substituting

v = u + at

32 = 0 + a x 0.40

a = 80 rad/s²

Angular acceleration is 80 rad/s²

We have equation of motion s = ut + 0.5 at²

Initial angular velocity, u = 0 rad/s

Angular acceleration, a = 80 rad/s²

Time, t = 0.4 s

Substituting

s = ut + 0.5 at²

s = 0 x 0.4 + 0.5 x 80 x 0.4²

s = 6.4 rad

Angular displacement = 6.4 rad

$\texttt{Number of revolutions = }\frac{6.4}{2\pi}=1.02$

Number of revolutions undergone is 1.02