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Rolling
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Rotation and Translation A rolling wheel is moving forward with kinetic energy. The velocity is measured at the center of mass. K CM = ½ m v 2K CM = ½ m v 2 A rolling wheel is rotating with kinetic energy. The axis of rotation is at the center of mass. K rot = ½ I 2 v
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No Slipping A wheel can slide, but true rolling occurs without slipping. As it moves through one rotation it moves forward 2 R. x = 2 R R v = 2 R/T = R v
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Point on the Edge A point on the edge moves with a speed compared to the center, v = r. Rolling motion applies the same formula to the center of mass velocity, v = R. The total velocity of points varies by position. v = 2v CM v CM v = 0
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Rolling Energy The energy of a rolling wheel is due to both the translation and rotation. The velocity is linked to the angular velocity. The effective energy is the same as a wheel rotating about a point on its edge. Parallel axis theoremParallel axis theorem
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Energy Conserved A change in kinetic energy is due to work done on the wheel. Work is from a forceWork is from a force Force acts as a torqueForce acts as a torque Rolling down an incline the force is from gravity. Pivot at the point of contactPivot at the point of contact The potential energy is converted to kinetic energy. F = mg v R
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Rolling Friction A perfect wheel has no sliding, so there should be no friction. Real wheels and ground press together. Points with some velocity Forward component generates friction next v > 0
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