10_1425_web_Lec_20_MoreRotationalDynamics

10_1425_web_Lec_20_M - More Rotational Dynamics Physics 1425 Lecture 20 Michael Fowler UVa Clicker Question A uniform rod is free to rotate in a

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More Rotational Dynamics Physics 1425 Lecture 20 Michael Fowler, UVa
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Clicker Question A uniform rod is free to rotate in a vertical plane about a frictionless hinge at one end. It is released from rest at an angle of 30°. ( I = (1/3) ML 2 , τ = Mg ( L /2)cos30°) The initial downward acceleration of the free end of the rod is: A. equal to g B. greater than g C. less than g 30°
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Rotational Kinetic Energy Imagine a rotating body as composed of many small masses m i at distances r i from the axis of rotation. The mass m i has speed v = ω r i , so KE = ½ m i r i 2 ω 2 . The total KE of the rotating body ( assuming the axis is at rest ) is ( ) 22 2 11 ii i K mr I ωω = =
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Torque Power If a net torque τ is acting on a rotating body, the net power is the rate of change of rotational energy So the rate of working of the torque, power = τω , its value x the angular velocity. Total work done over some time period is This is just like Fdx in linear motion. ( ) 2 1 2 (recall ) dd II I I dt dt ω ωα ωτ τ α = = = = d dt dt d dt θ τω τ θ = ∫∫
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Work Done by a Torque Suppose the torque is a force F acting at a distance r from the center as shown. If the disk turns through an angle d θ , the force acts through a distance ds = rd so does work Fds = Frd .
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This note was uploaded on 12/07/2011 for the course PHYSICS 1425 taught by Professor Michaelfowler during the Spring '10 term at UVA.

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10_1425_web_Lec_20_M - More Rotational Dynamics Physics 1425 Lecture 20 Michael Fowler UVa Clicker Question A uniform rod is free to rotate in a

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