Rotational Kinematics - Angular Acceleration

[nx01]

Homework Statement

A phonograph turntable with an initial angular velocity of 78 rpm continues turning for 40 rotations after being switched off. What is the angular deceleration of the turntable? Assume constant angular deceleration.

Homework Equations

$\alpha$=($\omega$-$\omega$₀)/t

θ-θ₀=1/2($\omega$₀+$\omega$)t

The Attempt at a Solution

t = (40 rot - 0 rot) / 1/2(78 rpm + 0 rpm) = 40/39 min

$\alpha$ = (0 rpm - 78 rpm) / (40/39 min) = -76.05 rpm²

The answer needs to be in rad/s²

(-76.05 rpm²)(2∏ rad/rot)(min²/s²)=-7.96 rad/s²


The back of the book tells me this answer is incorrect. I would appreciate any insight into the error(s) I am making.

Thank you!

 

[hjelmgart]

sure you made the right unit convertion? I get 0.84 rad/s^2 is that what you needed? Else I think the mistake lies elsewhere.

 

[nx01]

Hi hjelmgart,

Thanks for your reply. I'm pretty sure that my error lies in the unit conversion - did you do what I did in the conversion in the original post, or something else?

 

[hjelmgart]

Not entirely. I don't understand how you reached that result also. rpm = rev/min

(1/min)^2 = 1/(60min/s)^2

rev^2 = (2*Pi)^2

 

[nx01]

Ah, I wasn't squaring the seconds unit when converting. Thanks!