A uniform disk of radius 0.2 m and mass m = 16 kg is mounted on a nearly frictionless axle. A string is wrapped tightly around the disk and pulled with a constant force of F = 1 N. After a while the disk has reached an angular speed of !0 = 1.2 rad/s. What is its angular speed 1.5 s later?

ω = 2.13rad/s

Explanation:

Given

F = 1N = force applied, m = 16kg, R = 0.2m

ωo = 1.2rad/s

t = 1.5s

ω = ?

Where

α = angular acceleration

ωo = initial angular speed

And ω = angular speed at a later time t

For a rigid body rotating about an axis

τ = FR= I×α

I = 1/2×MR² for a uniform disk

FR = (1/2×mR²)×α

= 1/2×mR²×(ω – ωo)/t

Therefore

FR= 1/2×mR²×(ω – ωo)/t

2Ft/mR = ω – ωo

ω = 2Ft/mR + ωo

ω = 2×1×1.5/(16×0.2) + 1.2 = 2.13 rad/s