A flat disc of mass m = 1.8 kg radius r = 0.2m lies on a frictionless horizontal table. A string wound around the cylindrical surface of the disc exerts a force of 3 Newtons in the northerly direction (Fig.). Find the acceleration (magnitude and direction) of the center of mass a and the angular acceleration α about the center of mass. Is a = r α ? Explain.
Text Solution
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Sol. The equations of motion are
f = ma,
fr = I α ,
where I = mr 2 /2, giving
a = 
= 1.7 m/s 2 α = 
= 17 rad/s
2 .
The direction of a is the same as that of f . It is seen that a ≠ α r. This is because as the disc lies on its flat surface the two motions are not related even through they are due to the same force.
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