Question

A turntable that spins at a constant 77.0 rpm takes 3.50 s to reach this angular speed after it is turned on. Find its angular acceleration (in rad/s^2), assuming it to be constant, and the number of degrees it turns through while speeding up.

Answer 1

(a)

From the rotational kinematic equation the formula for angualr accleration is

   α = (ω2 - ω1)/t

since initially turntable is at rest so its initial angualr speed is zero

   α = ( 77 rpm - 0)/ 3.5 s

     = 77 rpm( 2 pi rad/ 60 s)/ 3.5 s

     = 8.059 rad/s/3.5s

    = 2.30 rad/s^2

(b)

Angular displacement can be expressed as

                            θ = (1/2)α t^2

                               = (1/2)2.30 rad/s^2( 3.5 s)^2

                                    = 14.0875 rad = 4.484π

The number of degrees it turns through while speeding up is

          θ = (4.484π ) (180/π)

          θ = 807.15 degrees