Constant Rotation Now that we know how to define the angular position, we can examine rotational motion. Consider the lab equipment using a view from above. Data Studio

Constant Rotation Since the graph is linear and contains (0,0) Every second, the angular position increases by # rad

Constant Rotation Since the graph is linear and contains (0,0) omega

Constant Rotation omega Notice that all parts of the object have the same angular position, angular displacement, and angular velocity! Angular Displacement

Constant Rotation What if the object did not start at 0 angular position? Constant angular velocity

Constant Rotation What does the graph look like if the object is rotated clockwise? Data Studio Angular velocity is a vector! Counterclockwise rotation = + Clockwise rotation = - Right Hand Rule – curl the fingers of your right hand in the direction of rotation. The vector is in the direction of your outstretched thumb. The object rotates around the vector.

Constant Rotation How do you relate the angular velocity of the object to the linear velocity of a particular point?

Constant Rotation How do you relate the angular velocity of the object to the linear velocity of a particular point? Since the object is moving with constant linear speed as well as constant angular velocity Radian measure For one complete rotation

Rolling at Constant Velocity Consider a disk rolling without slipping at a constant velocity. While most points both rotate and move linearly, the center of mass is only moving linearly with a constant speed

Both a point on the outside of the disk and the center of mass must move a distance s for the disk to roll without slipping! Rolling at Constant Velocity

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 have the same linear speed for the disk to roll without slipping! Radian measure Rolling at Constant Velocity