Rolling. Rotation and Translation  A rolling wheel is moving forward with kinetic energy.  The velocity is measured at the center of mass. K CM = ½.

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Presentation transcript:

Rolling

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 

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

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

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

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 

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