Answer:
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
