This question was on my homework last week and I had trouble figuring out how to plug the variables in. Could anyone show me a step-by-step answer?

Question

To start his lawn mower, Bob pulls on a cord that is wrapped around a pulley. The pulley has a moment of inertia about its central axis of I = 0.650 kgm2 and a radius of 5.40 cm. There is an equivalent frictional torque impeding his pull of

T = 0.480 m·N. To accelerate the pulley with an angular acceleration of 4.50 radians per second squared, a) how much torque does Bob need to apply to the pulley? b) How much tension must the cord be able to withstand?

Answer 1

The statement that there is a "equivalent frictional torque impeding his torque" is confusing. What he means is that there is a frictional force acting at the same radius resulting in a torque of .48 N-m.

2nd Law for rotation says the net torque is the moment of inertia times the angular acceleration:

τ - .48 = Iα

τ = .48 N-m + (.65 kgm²)(4.50 rad/s²)

The cord has to supply the force such that Fr = τ or Tension in Newtons = τ/.054 m

Hope that helps.