Torque problem - game show wheel

[FlipStyle1308]

A solid wheel on a game show is given an initial angular speed of 1.25 rad/s in the counterclockwise direction. It comes to rest after rotating through 3/4 of a turn.

Find the torque exerted on the wheel given that it is a disk of radius 0.73 m and mass 6.4 kg.

I got 0.5654 as the answer, but it's not correct. Anyone able to help?

 

[dav2008]

Can you show how you obtained that answer so we can see where you made your mistake?

 

[FlipStyle1308]

I used mr^2 = (6.4)(0.73)^2 = 3.41056. Then I plugged that into Wf^2 = Wi^2 + 2 (angular acceleration) (delta theta) => 0 = (1.25)^2 + (angular acceleration) (1.5 pi) => 0.1658. Then I multiplied that by 3.41056 to get 0.5654 as my torque.

 

[dav2008]

mr² is the moment of inertia for a point object about a point a distance r away.

You are not dealing with a point, but with an entire disc. The moment of ineria of a disc about the central axis is a slightly different expression.

Here is a helpful website that shows the moments of inertia of various objects: http://hyperphysics.phy-astr.gsu.edu/hbase/mi.html#cmi

You can either memorize the formulas or derive them by integrating, depending what your teacher/professor requires you to do.

 

[FlipStyle1308]

Okay, so I use T = 1/2 mr^2. Then once I get the inertia, do I still multiply it by 0.1658, the angular acceleration I got, in order to get torque?

 

[dav2008]

Yes, that looks right.

 

[FlipStyle1308]

Wait...how do I incorporate the 3/4 of a turn into this problem? Do I translate that to 1.5 pi?

 

[dav2008]

Yes, you already encorporated that into your work earlier:

I used mr^2 = (6.4)(0.73)^2 = 3.41056. Then I plugged that into Wf^2 = Wi^2 + 2 (angular acceleration) (delta theta) => 0 = (1.25)^2 + (angular acceleration) (1.5 pi) => 0.1658. Then I multiplied that by 3.41056 to get 0.5654 as my torque.

All of that work is right, except that you used mr² instead of 1/2mr²

Edit: Your answer for acceleration of .1658 looks right but you probably made a typo when posting the equation that's underlined, since your previous equation of "Wf^2 = Wi^2 + 2 (angular acceleration) (delta theta)" is right.

 

[FlipStyle1308]

Will my answer end up negative or positive? Cuz my result for the angular acceleration is negative.

 

[dav2008]

If you define clockwise as negative and counterclockwise as positive it makes sense that the torque is negative because it is acting in the clockwise direction, causing the wheel to stop. You just have to be consistant as to the signs you use.

You are finding the torque excerted that causes the wheel to stop, right? That's what you solved for. If you are trying to find the torque that the person who spun the wheel applied then I don't think you have enough information.

 

[FlipStyle1308]

Never mind, I got it. Thank you for your help!