Perfect Rolling (no sliding!) Consider a disk rolling without slipping with a Uniform Acceleration. While most points both rotate and move linearly, the center of mass is moving linearly with a constant acceleration

Perfect Rolling (no sliding!) Rolling Condition – must hold for an object to roll without slipping. Both a point on the outside of the disk and the center of mass must move the same linear distance, with the same linear velocity and the same linear acceleration for the disk to roll without slipping! Radian measure

Perfect Rolling (no sliding!) One way to view rolling is as a combination of pure rotation and pure translation. Pure Rotation Pure Translation Rolling The point that is in contact with the ground is not in motion with respect to the ground!

Perfect Rolling (no sliding!) Rolling The point that is in contact with the ground is not in motion with respect to the ground! Since the bottom point is at rest with respect to the ground, static friction applies if any friction exists at all. Static friction does not dissipate energy. However, there usually is rolling friction caused by the deformation of the object and surface as well as the loss of pieces of the object. Rolling friction does dissipate energy.

If the disk is moving at constant speed, there is no tendency to slip at the contact point and so there is no frictional force. Both act through the axis of rotation and therefore both exert no torque!

If, however, a force acts on the disk, like when you push on a bike pedal, then there is a tendency to slide at the point of contact so a frictional force acts at that point to oppose that tendency. The force of friction does apply a torque which results in the rolling object accelerating both linearly and rotationally!

Perfect Rolling (no sliding!) Consider a rolling object smoothly accelerating down a hill. If the hill was frictionless, there would not be a force of static friction and therefore the object would slide down the hill instead of roll!

Perfect Rolling (no sliding!) Consider a rolling object smoothly accelerating down a hill.

Perfect Rolling (no sliding!) Consider a rolling object smoothly accelerating down a hill. F N and F g exert no torque since they act through the axis of rotation (cm)

A hoop and a disk with identical masses and radii roll down an incline. How do their motions compare? Perfect Rolling (no sliding!) SoSince they have the same distance to move and both start from rest,

Perfect Rolling (no sliding!) Kinetic Energy ( E k ) - The ability to produce change due to an object’s motion. Translational (Linear) Kinetic EnergyRotational Kinetic Energy

Perfect Rolling (no sliding!) Just as rolling motion can be viewed as a combination of pure rotation and pure translation, the kinetic energy of a rolling object can be viewed as a combination of pure rotational kinetic energy and pure translational kinetic energy. Pure Rotation Pure Translation

A hoop and a disk with identical masses and radii roll down an incline. How do their motions compare? Perfect Rolling (no sliding!) So More of the disk’s kinetic energy will be translational so, System = Object, Incline, Earth But