# Torque problem (rod)

1. A uniform horizontal rod of mass 3 kg and length 0.25 m is free to pivot about one end. The moment of inertia about an axis perpendicular to the rod and through the Center of Mass is given by I = $$\frac{ml^{2}}{12}$$

If 8.9 force at an angle of 40 degrees to the horizontal acts on the rod, what's the magnitude of the resulting angular acceleration?

http://img301.imageshack.us/img301/3267/torqueproblemscy6.jpg [Broken]

2. Here's what I did.

$$\sum$$ $$\tau$$ = I $$\alpha$$ = ?

$$\tau$$ = LFsin$$\theta$$ = I $$\alpha$$

Given an I, but the wrong I, I substituted the moment for a rod spinning on the edge, not the center of mass. Giving me...

$$\tau$$ = $$\frac{m^L{2}}{3}$$ $$\alpha$$

I rearranged and plugged in my values for the alpha, and I ended up with...

1/3 $$\alpha$$ = $$\frac{Fsin\Theta}{ML}$$

$$\alpha$$ = 3 * $$\frac{8.9 * sin (40)}{3 * 0.25}$$

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if you break the force vector into components, you get that the horizontal compontant is Fcos*theta and the vertical component is Fsin*theta

in your torque diagram, the weight of the rod is at the center (r=l/2) and causes the rod to want to go clockwise. the vertical component of the force vector (Fsin*theta) wants to make the rod go counterclockwise.

this means that the sum of the torques should equal: (Fsin*theta*l)-(m*g*l/2)

its l/2 because the weight of the rod comes from the center of the rod, at a radius of l/2

So, given that I can apply the same idea I was going for to find out Alpha and set the sum of the torques equal: I * alpha (angular acceleration), or would I have to do two separate equations and find a resultant vector for the acceleration plugging in the two separate components of "F" into that equation you have presented.

So Just set the radii to (0.25/2) because at w_r you are at the CoM? This would give something along the lines of T = w_r - Fsin(40) and set that to I alpha? replacing the radii in I with (0.25/2)???