Question

A:

What is the angular momentum of a figure skater spinning at 3.4 rev/s with arms in close to her body, assuming her to be a uniform cylinder with a height of 1.4 m , a radius of 15 cm , and a mass of 48 kg ?

**Express your answer using three significant figures and include the appropriate units

B:

How much torque is required to slow her to a stop in 4.5 s , assuming she does not move her arms?

**Express your answer using three significant figures and include the appropriate units

Answer 1

Moment of inertia of solid cylinder is give by

R = 15 cm = 0.15 m

Hence

I = 0.54 Kg.m²

Angular momemtum is given by

L = I x

here = 3.4 rev/s = 3.4 x 2 rad/s = 21.36 rad/s

Hence

L = 0.54 x 21.36 = 11.5 kg m² s⁻¹

b)To stop in 4.5 s , angular deceleration is given by kinematic equations of Newton in rotational form.

here final angular speed = 0

Hence

0 = 21.36 + x 4.5

= - 4.7466 rad/s²

So, Torque required = I x

                             = 0.54 x 4.7466

                              = 2.56 N.m