Question

What is the angular momentum of a figure skater spinning at 3.2rev/s with arms in close to her body, assuming her to be a uniform cylinder with a height of 1.5m , a radius of 16cm , and a mass of 55kg?

How much torque is required to slow her to a stop in 4.4s , assuming she does not move her arms?

Answer 1

angular speed , w = @/t

w = 3.2* 2*pie / 1sec= 3.2*2*pie rad/sec

moment of interia of cylinder , I = (1/2)*M*R²

I = (1/2)*55*(0.16)²                                                 ( R = 16 cm = 0.16m)

I = 0.704 kg-m²

angular momentum, L = I*w

L = 0.704*2*3.14*3.2

L = 14.14 kg-m² / s

B) torque = I*@                        (@ = angular acceleration)

           = I* ( dw/dt)

           = 0.704*( 2*3.14*3.2/ 4.4)

             = 3.229 N-m