Lecture214Week7

Lecture214Week7 - This Week Moving in circles Angular...

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This Week Moving in circles Angular momentum Spinning at the Olympics Torques Why is a wrench useful? Center of Gravity Useful info for crossing Niagara falls on a wire The New Hubble Telescope Views of Saturn 12/09/11 Physics 214 Fall 2011 1
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12/09/11 Physics 214 Fall 2011 2 Physics 214 Fall 2009 General case of motion In general the motion of an object consists of translation and rotation. Translation we have dealt with in straight line motion A wheel is an excellent example of rotation We define an axis and counterclockwise is positive. One full circle = 360 0 = 2π radians Circumference = 2πR Time for one revolution = 2πR/v 57.3 0 v R +
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12/09/11 Physics 214 Fall 2011 3 Physics 214 Fall 2009 3 Rotational Motion Consider an object moving in a circular path. It has velocity, acceleration, kinetic energy and momentum but these are not the simplest variables Displacement we use the angle θ measured in radians Angular velocity ω = Δθ/Δt Angular acceleration α = Δω/Δt 1 revolution/sec = 2π radians/sec Since the time for one revolution is 2πr/v = 2π/ω then v = rω so Δv = rΔω and Δv/Δt = rΔω/Δt and a = rα All parts of a rotating wheel have the same ω but The further from the center the bigger is v θ v R
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12/09/11 Physics 214 Fall 2011 4 Physics 214 Fall 2009 Constant angular acceleration Apart from changing variables the equations are identical to linear motion with constant acceleration Displacement d θ Velocity v = Δd/Δt ω = Δθ/Δt Acceleration a = Δv/Δt α = Δω/Δt Constant v = v 0 + at ω = ω 0 + αt d = v 0 t + 1/2at 2 θ = ω 0 t + 1/2αt 2 v 2 = v 0 2 + 2ad ω 2 = ω 0 2 +2αθ d = ½(v + v 0 )t θ = ½(ω + ω 0 )t Once again all variables except time can be positive or negative
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12/09/11 Physics 214 Fall 2011 5 Physics 214 Fall 2009 Forces and torques If we apply a force to a bicycle wheel that is free to rotate for a given force it is easier to rotate the wheel the further you are from the axle. In the picture shown below each of the single weights on it’s own will cause the rule to rotate but the two together can be balanced. A force applied to an object, in general makes that object rotate and the action of the force we call a TORQUE and Τ = FL where L is the perpendicular distance to the line of action of the force. Once again + is counterclockwise and – is clockwise and the net torque is sum of all torques.
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12/09/11 Physics 214 Fall 2011 6 Physics 214 Fall 2009 Using a wrench In our everyday life we are limited in the force we can apply but if we increase the lever arm we can increase the torque. We can turn a very tight nut by applying a force F at a large radius R If the radius of the nut is r then to just move the nut FR = F f r so if R/r = 30 then F s /F = 30 The work done is the same because in one turn 2πRF = 2πrF s F R F f
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12/09/11 Physics 214 Fall 2011 7 Physics 214 Fall 2009 Center Gravity There is a point associated with any body that allows it to be balanced by a single force upward without any rotation.
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Lecture214Week7 - This Week Moving in circles Angular...

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