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Unformatted text preview: Lecture 14 Work Done by Torque Moment of Inertia Angular Momentum Physics 111, Summer 2011, July 7, Lecture 14 Summary 2 The average angular acceleration is the change in angular velocity divided by the change in time: The most convenient way is to measure the angle θ not in degrees, but in radians (abbreviated rad ): The average angular velocity is the ratio of the angular displacement over change in time: Tangential velocity (speed) in rotational motion: 3 . 57 28 . 6 360 2 360 1 = = = π rad t t t Δ Δ = − − = θ θ θ ω 1 2 1 2 ω r v = tan t t t Δ Δ = − − = ω ω ω α 1 2 1 2 Tangential acceleration vs. angular acceleration: α r a = tan Measuring the angle in radians, it’s easy to keep the ratio: θ r l = Acceleration in rotational motion may contain two components: R a a a r r r + = tan ( ) s rad / ( ) s m / ( ) 2 / s rad Torque is a vector that measures the tendency of a force to rotate an object about some axis or center (the unit is N ⋅ m) θ τ sin Fr = Physics 111, Summer 2011, July 7, Lecture 14 Work Done by Torque 3 l F work Δ = θ θ Δ = Δ Δ = Δ r l or r l The work done by torque when rotating a wheel about a fixed axis can be shown by angular quantities. θ Δ = Δ = Fr l F work rF = τ Because The work done by a constant torque is the product of torque and the angular displacement. θ τ Δ = work θ Δ l Δ ° 90 Physics 111, Summer 2011, July 7, Lecture 14 4 Work Done by Torque An engine with a power of 50,000 W started to rotate a wheel and after 0.1 s was disconnected from the wheel. If the wheel during this time was turned by 270 , what torque was applied to the wheel? θ τ Δ = work J s W time power work 5000 ) 1 . )( 000 50 ( ) )( ( = = = 1. Work done by the engine: 3. Torque: 2. The angle in radians: m N rad J work ⋅ = = Δ = 8 . 1063 7 . 4 5000 θ τ rad rad 7 . 4 / 3 . 57 270 = = Δ θ time work power = Physics 111, Summer 2011, July 7, Lecture 14 5 Rotational Dynamics: Torque and Rotation α mr ma ma F = = = tan is the angular acceleration α α α τ 2 ) )( ( mr r mr Fr = = = ( ) α τ ∑ ∑ = 2 mr Newton’s second law for a rotating object: Torque: The sum of various torques is the total torque: is the sum of the masses of each particle in the object multiplied by the square of the distances of that particle from the axis of rotation.the square of the distances of that particle from the axis of rotation....
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 Summer '08
 B
 Angular Momentum, Inertia, Kinetic Energy, Momentum, Work, Moment Of Inertia, Rigid Body, Angular Acceleration

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