# Rotational motion of a disc

#### public_enemy720

One more problem on a tough worksheet...I have tried it for a while, but can't find an equation(s) suitable for the problem...

A constant force of 12N is applied to the axle of a disc rolling along a flat plane. The disc has mass m=22kg, diameter D=.50m, and rotational inertia I=.688kgm^2. What is the linear speed of the center of the disc, V, after it has rolled for 12m?

I drew a free body diagram, and I know that the sum of the moments is equal to I times alpha, and I know the good ol' F=ma. But I can't seem to be able to find an acceleration with what I am given. A hint would be wonderful.

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#### public_enemy720

Oh boy...I went somewhere, but I don't know if it was right. Here is what I did:

I used m*a=f-f(friction) and friction*radius = I*alpha. Alpha is equal to a*r, so I plugged that in to make friction times radius = I*a*radius.

Plugging that in to m*a=F-f(friction) i got:

This is rather confusing, but I think it is somewhat correct. Any suggestions or gross errors on my part?

#### OlderDan

Homework Helper
public_enemy720 said:
Oh boy...I went somewhere, but I don't know if it was right. Here is what I did:

I used m*a=f-f(friction) and friction*radius = I*alpha. Alpha is equal to a*r, so I plugged that in to make friction times radius = I*a*radius.

Plugging that in to m*a=F-f(friction) i got:

This is rather confusing, but I think it is somewhat correct. Any suggestions or gross errors on my part?
Right idea, but alpha does not equal a*r. alpha and a are certainly related and you need that relationship, but that is not it.

#### vijay123

Homework Helper
vijay123 said:
$$a_{T}=\alpha \cdot r$$, i.e. tangential acceleration equals angular acceleration times radius.

#### minhtrietle

total K = (1/2)*m*v^2 + (1/2)*I*w^2

actually you don't have to use I = 0.688 which is given if you know the I of the disk is (1/2)*m*r^2.

plug all in, find out K = 3/4 * m * v^2

next,

the work does on the wheel also equals to the total K above. W = F*s = 12*12 = 144J

solve for v.

Good luck.

Minh T. Le

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