Question

A record is spinning with an initial angular velocity of ω₀ = 8.54rad/s. The record is decelerating due to an angular acceleration of α = -1.75rad/s². (a) How long does it take for the record to stop spinning? (b) Now assume that there was a notch on the record, where the initial value was at θ₀ = 0^o before it started to decelerate. What is the position, θ, of the the notch when the record stops rotating (give answer in 0^o to 360^o)?

Answer 1

(a) Given that -

w0 = 8.54 rad/s

alfa = -1.75 rad/s^2

Time to stop the record, t = ?

when the record stops, w = 0

use the expression -

w = w0 + alfa*t

=> 0 = 8.54 - 1.75*t

=> t = 8.54 / 1.75 = 4.88 s

(b) We have to determine the total angle travelled by the record in this case.

theta = w0*t + (1/2)*alfa*t^2 = 8.54*4.88 - 0.50*1.75*4.88^2 = 41.67 - 20.84 = 20.83 radians

convert this in degrees.

theta = (20.83 x 360) / (2 x 3.141) = 3.316 x 360 deg.

So, the position of the notch = 0.316 x 360 = 113.8 deg.

[We simply donot consider the value which is integral multiple of 360 deg.]