Question

A turntable that spins at a constant 74.0 rpm takes 3.10 s to reach this angular speed after it is turned on. Find its angular acceleration (in rad/s2), assuming it to be constant, and the number of degrees it turns through while speeding up.

Answer 1

`2.5 rad/s^2, 688^(\circ)`

Step-by-step explanation:

The angular acceleration is given by:

`\alpha = (\omega_f - \omega_i)/(t)`

where

`\omega_f = 74.0 rev/min \cdot ((2\pi rad/rev)/(60 s/min))=7.75 rad/s` is the final angular speed

`\omega_i = 0` is the initial angular speed

t = 3.10 s is the time interval

Solving the equation,

`\alpha = (7.75 rad/s - 0)/(3.10 s)=2.5 rad/s^2`

Now we can find the angular displacement by using:

`\theta = \omega_i t + (1)/(2)\alpha t^2`

Substituting,

`\theta=0+(1)/(2)(2.5 rad/s^2)(3.10 s)^2=12.0 rad`

In degrees:

`\theta = (12.0 rad)/(2\pi)\cdot 360^(\circ)=688^(\circ)`