Sliding vs Rolling Motion

Wheels have both translational and rotational motion (2 dynamics here).

Three types of Motion

1. Pure Rolling (no slipping between wheel and surface)
   • v=rw
2. Pure Sliding (rotation is prevented)
   • w=0 and v != rw
3. Sliding and Rotation
   • w != 0 and v != rw

Examples

Two wheeled cart

Tips

1. Draw 2 FBDs separating out parts of the system (don’t forget about the rotational inertia of the wheel)

• Remember to add the traction force to the wheel (torque force) to the contact point with the surface
• You have torque when you have a hinge point or some force acting on some lever arm o a point of rotation

1. Find the translational acceleration using FBDs of two systems
2. Using the system of equations find the equivalent mass (terms with an acceleration attached to it)
3. Use the equivalent mass and KE to solve for v