10_1425_web_Lec_19_RotationalDynamics

# 10_1425_web_Lec_19_RotationalDynamics - Rotational Dynamics...

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Rotational Dynamics Physics 1425 Lecture 19 Michael Fowler, UVa

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Rotational Dynamics Newton’s First Law: a rotating body will continue to rotate at constant angular velocity as long as there is no torque acting on it. Picture a grindstone on a smooth axle. BUT the axle must be exactly at the center of gravity— otherwise gravity will provide a torque, and the rotation will not be at constant velocity! A
How is Angular Acceleration Related to Torque? Think about a tangential force F applied to a mass m attached to a light disk which can rotate about a fixed axis. (A radially directed force has zero torque, does nothing.) The relevant equations are: F = ma , a = r α , τ = rF . Therefore F = ma becomes τ = mr 2 α Vhas zero F r Light disk m axle

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Newton’s Second Law for Rotations For the special case of a mass m constrained by a light disk to circle around an axle, the angular acceleration α is proportional to the torque τ exactly as in the linear case the acceleration a is proportional to the force F : τ = mr 2 α F = ma The angular equivalent of inertial mass m is the moment of inertia mr 2 .
More Complicated Rotating Bodies

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10_1425_web_Lec_19_RotationalDynamics - Rotational Dynamics...

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