Answer to Question #308827 in Physics for Fish

Question

A drum rotates around its central axis at an angular velocity of 12.60 rad/s. If the drum then slows at a constant rate of 4.20 rad/s2.

(a) how much time does it take?

(b) through what angle does it rotate in coming to rest (3.0s , 18.9 rad)

Answer 1

a) The angular speed of the drum at any time $t$ is given as follows:

$$\omega = \omega_0-\alpha t$$

where $\omega_0 = 12.6rad/s, \alpha = 4.2rad/s^2$. When it comes to rest $\omega=0$. The corresponding time is then:

$$t = \dfrac{\omega_0}{\alpha} = \dfrac{12.6rad/s}{4.2rad/s^2} = 3.0s$$

b) The radial distance is:

$$\phi = \omega_0 t-\dfrac{\alpha t^2}{2} = 12.6rad/s\cdot 3s - \dfrac{4.2rad/s^2\cdot (3s)^2}{2} =18.9rad$$