Answer to Question #308827 in Physics for Fish

Question #308827

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)

1
Expert's answer
2022-03-10T11:16:08-0500

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


ω=ω0αt\omega = \omega_0-\alpha t

where ω0=12.6rad/s,α=4.2rad/s2\omega_0 = 12.6rad/s, \alpha = 4.2rad/s^2. When it comes to rest ω=0\omega=0. The corresponding time is then:


t=ω0α=12.6rad/s4.2rad/s2=3.0st = \dfrac{\omega_0}{\alpha} = \dfrac{12.6rad/s}{4.2rad/s^2} = 3.0s

b) The radial distance is:


ϕ=ω0tαt22=12.6rad/s3s4.2rad/s2(3s)22=18.9rad\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

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