Torque Spool

Who understands this torque problem?
In fig. 10.4, a solid cylinder of 3 cm radius is positioned on a frictionless plane inclined at 30 degrees above horizontal. A force F is exerted by a string wrapped around the spool. When F has a certain critical value the center of mass of the spool does not move. When this is the case, what is the angular acceleration of the spool.
I’m not too sure about the approach here.

The force will be equal in value to the force pulling the cylinder down, as the center of mass is not moving.
Therefore: F = mgsin(30) = 0.5mg
Now, let’s get the moment of intertia of the cylinder:
I = 0.5mr^2
Now, use the equation:
Fr = Ia, where a is angular acceleration
0.5mgr = 0.5mr^2 * a
g = ra
a = g/r
Assuming g = 10m/s^2, r = 0.03m
a = 10m/s^2 / 0.03m = 333.3 rad/s^2
This value seems a bit extreme, though.
Sound Performance Quick Spool Valve Results on Precision 6765 Billet!!!
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GALVAN T-3 SPARE SPOOL FOR TORQUE 3 FLY REEL GREEN 1/2 OFF LINE + FREE BACKING $142.00 |
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GALVAN T-3 SPARE SPOOL FOR TORQUE 3 FLY REEL BRONZE 1/2 OFF LINE + FREE BACKING $142.00 |
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GALVAN T-5 SPARE SPOOL FOR TORQUE 5 FLY REEL CLEAR 1/2 OFF LINE + FREE BACKING $160.00 |
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GALVAN T-5 SPARE SPOOL FOR TORQUE 5 FLY REEL GREEN 1/2 OFF LINE + FREE BACKING $160.00 |
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Galvan Torque spare spool 10 clear With 1/2 off Line $204.50 |
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Tomioka Racing Subaru Exhaust Manifold – Equal Length $690.00 Tomioka Racing equal exhaust manifold is made of all stainless steel and built based on its consistently excellent performance results, and high quality finish with 4-2-1 connectors. With smooth flowing joining faces thus removing any kind of gas flow restriction and provides excellent spool up, smoother delivery of power, & increase in torque. The manifold is supplied with all manifold and turbo … |
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