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Rolling

Rolling. A rolling wheel is moving forward with kinetic energy. The velocity is measured at the center of mass. K 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 w 2. Rotation and Translation. w. v. No Slipping.

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Rolling

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  1. Rolling

  2. A rolling wheel is moving forward with kinetic energy. The velocity is measured at the center of mass. KCM = ½ mv2 A rolling wheel is rotating with kinetic energy. The axis of rotation is at the center of mass. Krot = ½ Iw2 Rotation and Translation w v

  3. No Slipping • A wheel can slide, but true rolling occurs without slipping. • As it moves through one rotation it moves forward 2pR. w v v = 2pR/T = wR R Dx = 2pR

  4. Point on the Edge • A point on the edge moves with a speed compared to the center, v = wr. • Rolling motion applies the same formula to the center of mass velocity, v = wR. • The total velocity of points varies by position. v =2vCM vCM v =0

  5. 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 theorem

  6. A change in kinetic energy is due to work done on the wheel. Work is from a force Force acts as a torque Rolling down an incline the force is from gravity. Pivot at the point of contact The potential energy is converted to kinetic energy. Energy Conserved v R F = mg q

  7. 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 v >0 next

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