# Chapter 8 - Problems - Page 317: 79

The skater does $69.7~J$ of work to pull in her arms while spinning.

#### Work Step by Step

We can use conservation of angular momentum to find the final angular velocity: $L_f = L_0$ $I_f~\omega_f = I_0~\omega_0$ $\omega_f = \frac{I_0~\omega_0}{I_f}$ $\omega_f = \frac{(2.50~kg~m^2)(10.0~rad/s)}{1.60~kg~m^2}$ $\omega_f = 15.6~rad/s$ The new angular velocity is $15.6~rad/s$ We can find the change in rotational kinetic energy: $\Delta KE_{rot} = \frac{1}{2}I_f~\omega_f^2 - \frac{1}{2}I_0~\omega_0^2$ $\Delta KE_{rot} = \frac{1}{2}(1.60~kg~m^2)(15.6~rad/s)^2 - \frac{1}{2}(2.50~kg~m^2)(10.0~rad/s)^2$ $\Delta KE_{rot} = 69.7~J$ Since the rotational kinetic energy increases by $69.7~J$, the skater does $69.7~J$ of work to pull in her arms while spinning.

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