Solving Rotational Motion: 4kg Disk & 4.0kg + 8.0kg Masses

[Mugen112]

Homework Statement

A disk with a mass of 4kg and a .20m radius is free to rotate about a horizontal axis. A 4.0kg mass and a 8.0kg mass are attached by a massless string, which is hung over the disk. If the string does not slip, what is the angular velocity of the disk after 2 seconds?

Homework Equations

Angular acceleration = change in angular velocity/change in time
I= 1/2mr^2
Angular velocity= tangential velocity/radius

The Attempt at a Solution

I took a picture of my work. It looks like I did everything right, but I'm not sure. I thought I would use inertia in my problem solving, but I didn't need it?? All I did was, I found the acceleration of the heavier block using the formula in the picture (which includes the mass of the disk). I took that acceleration, which should equal the tangential acceleration, and found the tangential velocity after 2 seconds. With the tangential velocity, I found the angular velocity using the radius of the disk shown in the picture. Found it to be 28 rads/sec which is about 44 revolutions per second. I think this would be pretty fast when dealing with only 4 and 8kg weights... Is this correct? If you can't make something out in the picture, let me know. THANKS!

 

[tiny-tim]

Hi Mugen112!

I don't follow what you've done … I particularly don't follow your T₁ - T₂ equation … you would need torque = rate of change of angular momentum.

But why bother to find T1 and T2 when the question doesn't ask for them?

Just use KE + PE = constant.

 

[Mugen112]

I figured it out! Thanks for the help!