Rotational motion of a spinning disk

[november1992]

Homework Statement

A spinning disk is rotating at a rate of 30 rad/s in the counterclockwise direction. The disk is slowing down at a rate of 6 rad/s2. Find the angle through which the disk has turned after 3 s in radians, degrees, and revolutions.

Homework Equations

θ=θi + ωi*t + αt^2

The Attempt at a Solution

So when i plugged the variables into the equation I got 36.

θ = 0 + 90 - 54 = 36

I thought the units were in radians so that's what I entered for the radians part and I also got 2062 degrees, and 5.71 revolutions. But I got the question wrong.

The answer was:

Angle through which wheel has turned (in radians) = 63 radians
(in degrees) = 3610.0000 degrees
(in revolutions) = 10.0300 revolutions

I don't understand what I did wrong.

 

[PeterO]

Homework Statement

A spinning disk is rotating at a rate of 30 rad/s in the counterclockwise direction. The disk is slowing down at a rate of 6 rad/s2. Find the angle through which the disk has turned after 3 s in radians, degrees, and revolutions.

Homework Equations

θ=θi + ωi*t + αt^2

The Attempt at a Solution

So when i plugged the variables into the equation I got 36.

θ = 0 + 90 - 54 = 36

I thought the units were in radians so that's what I entered for the radians part and I also got 2062 degrees, and 5.71 revolutions. But I got the question wrong.

The answer was:

Angle through which wheel has turned (in radians) = 63 radians
(in degrees) = 3610.0000 degrees
(in revolutions) = 10.0300 revolutions

I don't understand what I did wrong.

I see the question as:

Initial ω = 30,
Final ω = 12 [loses 6 each second for 3 seconds]
Average ω = (30 + 12)/2 = 21

21 for 3 seconds gives 63 radians.

I think there should have been a 1/2 factor in the "αt^2" term of your formula !


[Note: I left the rad/s unit out throughout for clarity]

 

[november1992]

aw man. I can't believe i missed that :/
thanks for the help.