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**Unformatted text preview: **Power; Rotational Energy • Power • Rotational work, power, and kinetic energy. Serway & Jewett 7.5, 10.4, 10.8 Recall: θ r s = ϖ r v t = α r a t = i i f t α ϖ ϖ + = αθ ϖ ϖ α ϖ θ θ 2 2 2 2 2 1 + = + + = i f i i f t t Power Power is the rate at which work is done: Average power = Work/time Instantaneous power: Average over an infinitesimal time dt, displacement ds ; the work is dW = F • ds , and power is units: 1 J/s =1 watt (W) v F ds F ⋅ = ⋅ = = dt dt dW P Rotational Work A bit of work, dW , is done in turning a nut through a tiny angle d θ : θ τ θ φ φ d d r F ds F dW ) sin ( ) sin ( = = = ⋅ = ds F φ r F ds = rd θ d θ θ τ d dW = θ τ ∆ = W So, and so for a constant torque, Power: dt d dt d dt dW P θ τ θ τ = = = ) ( (again, angular velocity must be expressed in radians/second). ϖ τ = P So, Quiz A power screwdriver is intended to provide a torque of 0.5 N·m while turning at 120 revolutions per minute. The minimum power needed from the motor will be about A) 60W B) 6 W C) 1 W Kinetic energy of a rotating rigid body:...

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