With the aid of a string, a gyroscope is accelerated from rest to 16 rad/s in 0.40 s. What is its angular acceleration in rad/s2? Approximately how many revolutions does it go through in the process?

Explanation:

Given that,

A gyroscope accelerated from rest

Initial angular speed ωi = 0

The gyroscope accelerated to

ωf = 16rad/s

time taken t = 0.4s

A. What is it's angular acceleration α?

Using equation of circular motion

ωf = ωi + αt

16 = 0 + 0.4α

16 = 0.4α

then, α = 16 / 0.4

α = 40rad/s2

The angular acceleration is 40rad/s².

b. Revolution θ?

Using circular motion equation

ωf² = ωi² + 2α∆θ

16² = 0² + 2×40∆θ

256 = 0 + 80∆θ

256 = 80∆θ

∆θ = 256 / 80

∆θ = 3.2 rad.

θf - θi = 3.2rad

The initial revolution Is zero, since it starts from rest

θ = 3.2rad

We know that, 1 rev = 2πrad

Then, θ = 3.2 rad × 1rev/2πrad

θ = 0.51 revolution

θ ≈ 0.5 revolution

So, gyroscope makes an approximately 0.5 revolution in 0.4 seconds