Question

A drum rotates around its central axis at an angular

velocityof 12.60rad/s. If the drum then slows at a constant rate
of4.20rad/s2, a) how much time does it take and b)
throughwhat angle does it rotate in coming to rest?

Answer 1

a)t= 3 s

b)θ = 18.9 rad

Step-by-step explanation:

Given that

Initial angular velocity ,ωi = 12.6 rad/s

Acceleration ,α = - 4.2 rad/s²

Final angular speed ,ωf = 0 rad/s

We know that

ωf =ωi + α t

t=Time

Now by putting the values

0 = 12.6 - 4.2 x t

`t=(12.6)/(4.2)\ s`

t= 3 s

We also know that

ωf² =ωi² + 2 α θ

θ=Angle

Now by putting the values

0² =12.6² - 2 x 4.2 x θ

`\theta=(12.6^2)/(2* 4.2)\ rad`

θ = 18.9 rad

a)t= 3 s

b)θ = 18.9 rad