Answer to Question #86208 in Mechanics | Relativity for godwina divila

Question

During a throw an athlete exerts a net average torque of 100 Nm on a discus
about its axis of spin. The mass of the discus is 2 kg and its radius of gyration
about its spin axis is 12 cm. If the discus was not spinning at the beginning of
the throw and the throwing action lasts for 0.2 s, calculate how fast (in
radians s-1) the discus is spinning when it is released.

Answer 1

$$\tau=\dfrac{dL}{dt}, \,\, L=I \omega,\,\, dL=dI \omega +I d\omega=I d\omega$$

$$\tau dt=I d\omega$$

$$I=mr^2$$

$$d\omega=\dfrac{\tau dt}{mr^2}=\dfrac{100\cdot 0.2}{2\cdot 0.12^2}\approx 694.44\, rad \cdot s^{-1}$$