Question

An ice skater has a moment of inertia of 5.0 kg · m2when her arms are outstretched, and at this time she is spinning at 3.0 rev/s. If she pulls in her arms and decreases her moment of inertia to 2.0 kg · m2, how fast will she be spinning?

Answer 1

Step-by-step explanation:

Given

Initial Moment of Inertia
`I_1=5 kg-m^2`

initial Spin
`N_1=3 rev/s`

`\omega _1=2\pi N_1=2\pi 3=6\pi rad/s`

Final Moment Moment of Inertia
`I_2=2 kg-m^2`

Conserving Angular momentum

`L_1=L_2`

`I_1\omega _1=I_2\omega _2`

`5* 6\pi=2* \omega _2`

`\omega _2=15\pi rad/s`

`N_2=(\omega _2)/(2\pi )`

`N_2=(15\pi )/(2\pi)=7.5 rev/s`