Why Is My Calculation of Angular Acceleration Incorrect?

[maniacp08]

When a turntable rotating at 33 1/3 rev/min is shut off, it comes to rest in 26 s. Assume constant angular acceleration.
(a) Find the angular acceleration.
rad/s2

(b) Find the average angular velocity of the turntable.
rad/s

(c) Find the number of revolutions it makes before stopping.
rev

For Part A I did:
omega = omega initial + alpha * t
omega = alpha * t
omega/t = alpha

(33.3 rev/min) / (26s) * (2Pi rad) / (1 rev) * (1 min) /(60s)
= .1341218402 rad/s^2 = approx .13 rad/s^2
but this is wrong.

For Part C:
displacement = omega initial + 1/2 alpha * t^2
= 1/2(.1341218402 rad/s^2)(26s)^2
=45.33318199 approx = 45 revolutions.

For Part B is it taking the average of initial omega velocity and final omega velocity?

 

[LowlyPion]

When a turntable rotating at 33 1/3 rev/min is shut off, it comes to rest in 26 s. Assume constant angular acceleration.
(a) Find the angular acceleration.
rad/s2

(b) Find the average angular velocity of the turntable.
rad/s

(c) Find the number of revolutions it makes before stopping.
rev

For Part A I did:
omega = omega initial + alpha * t
omega = alpha * t
omega/t = alpha

(33.3 rev/min) / (26s) * (2Pi rad) / (1 rev) * (1 min) /(60s)
= .1341218402 rad/s^2 = approx .13 rad/s^2
but this is wrong.

For Part C:
displacement = omega initial + 1/2 alpha * t^2
= 1/2(.1341218402 rad/s^2)(26s)^2
=45.33318199 approx = 45 revolutions.

For Part B is it taking the average of initial omega velocity and final omega velocity?

Isn't acceleration negative? (V goes to 0.)

Your equation for c) yields radians not revolutions.

b) yes. Initial angular velocity over 2.

 

[maniacp08]

Hmm, I put -.13 rad/s^2 but it was still wrong and as for part C I calculated to approx 71 revolutions and it was wrong. what else I did wrong?

Initial angular velocity / 2
initial angular velocity is = angular acc. * 1s correct?

 

[LowlyPion]

Hmm, I put -.13 rad/s^2 but it was still wrong and as for part C I calculated to approx 71 revolutions and it was wrong. what else I did wrong?

Initial angular velocity / 2
initial angular velocity is = angular acc. * 1s correct?

33.33 = 100/3
My calculation for angular acceleration is w = 2*π*f = 2*π*100/(3*60)

Since w = a*t => a = w/t = 2*π*100/(3*60*26) = -.13426 r/s²

Total radians = 1/2*a*t² = 45.38 radians

Revolutions = radians/(2*π) = 7.22 revolutions

It couldn't have been 71 revolutions because it only was going 33/min. At full speed it can't be over 33/2 since 26 sec is < 1/2 min.

w = 3.49 rad/s and half is 1.75 rad/sec

 

[maniacp08]

Oh, I guess I should've put more decimal places rather than just -.13 rad/s^2
and for part B, you are right it was 7.22, I saw it as 72.

Thanks for the clarification!

 

[LowlyPion]

Oh, I guess I should've put more decimal places rather than just -.13 rad/s^2
and for part B, you are right it was 7.22, I saw it as 72.

Thanks for the clarification!

Not sure what the number of significant digits are for your teacher. Perhaps there is something from class?

They ask for rad/sec² and that has to be a small fractional number.