Question

A turntable that spins at a constant 76.0 rpm takes 3.50 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

Answer: 2.27 rad/s², 796°

Step-by-step explanation:

Given,

time, t = 3.5 s

speed, w = 76 rpm

To start, we have to convert the speed to rad/s

76 rpm * 1/60 s * 2π rad/rev

= 7.96 rad/s

α = Δω / Δt

α = 7.96 rad/s / 3.5 s

α = 2.27 rad/s²

Θ = 1/2αt²

Θ = 1/2 * 2.27 * 3.5 * 3.5

Θ = 1/2 * 2.27 * 12.25

Θ = 1/2 * 27.8075

Θ = 13.90 rads

Converting back, we have,

Θ = (13.9 * 360°) / 2π rads

Θ = 796°

Therefore the angular acceleration is 2.27 rad/s²

The angle turned through is 13.9 rads or 796°

Answer 2

`\Delta \theta = 13.928\,rad\,(798.016\,^(\textdegree))`

Step-by-step explanation:

The angular acceleration of the the turntable is:

`\alpha = (\omega - \omega_(o))/(\Delta t)`

`\alpha = ((76\,(rev)/(min) )\cdot ((2\pi\,rad)/(1\,rev) )\cdot ((1\,min)/(60\,s) )-(0\,(rad)/(s) ))/(3.50\,s)`

`\alpha \approx 2.274\,(rad)/(s^(2))`

The change in angular position is:

`\Delta \theta = (1)/(2)\cdot \alpha \cdot t^(2)`

`\Delta \theta = (1)/(2)\cdot (2.274\,(rad)/(s^(2)) )\cdot (3.50\,s)^(2)`

`\Delta \theta = 13.928\,rad\,(798.016\,^(\textdegree))`