A disk of radius 2.02 cm and mass 1 kg is pulled by a string wrapped around its circumference with a constant force of 0.59 newtons. What is its angular acceleration to three decimal places?

24.752 rad/s²

Explanation:

From the question,

The expression of force on the disk is given as,

F = ma ... Equation 1

Where F = force, m = mass of the disk, a = acceleration of the disk.

In circular motion, recall that

a = αr ... Equation 2

Where α = angular acceleration, r = radius.

Substitute equation 2 into equation 1

F = m (αr)

F = mαr ... equation 3

make α the subject of the equation

α = F/mr ... Equation 4

Given: F = 0.59 N, m = 1 kg, r = 2.02 cm = 0.0202 m.

Substitute into equation 4

α = 0.59 / (1*0.0202)

α = 24.752 rad/s²