Question

A figure skater is spinning with an angular velocity of +12 rad/s. She then comes to a stop over a brief period of time. During this time, her angular displacement is +9.0 rad.

(a) Determine her average angular acceleration.

__rad/s2

(b) Determine the time during which she comes to rest.

___s

Answer 1

Answer:(a) According to the third law of angular motion, $\omega^2 =\omega_0^2+2\alpha \theta$

where $\omega_0 =12~rad/s$ and $\theta=9.0~rad$

Therefore, $0=12^2+2\alpha \times9$       $\Rightarrow$    $\alpha =-8~rad/s^2$

(b) according to the first law of angular motion,

$\omega =\omega _0+\alpha t$     $\Rightarrow$     $\Rightarrow$    $t=1.5~s$