1. Tangential and Centripetal Accelerations
Physics
Montwood High School

2. Relationship Between Angular and Linear Quantities
Tangential speed (vT) – the instantaneous linear speed at a point for a rotating object.
Point A and B both have the same angular velocity w. The tangential velocity at point A and B are not equal. The tangential velocity at point A is larger than the tangential velocity at point B.
For every turn, point A and B both move 360° or 2· rad, but they travel a different arc length s. Point A has to travel a greater distance s, so it has to have a greater tangential speed vT.
Equation: w in rad/s

4. Tangential and Angular Accelerations
As the angular speed w changes, so does vT. Therefore, as the angular acceleration a changes, so does the tangential acceleration aT.
Equation:
a in rad/s2

5. Centripetal Acceleration aC
Centripetal acceleration aC is the acceleration directed toward the center of a circle.
A force is needed to change the speed and/or direction of an object traveling on a circular path. This force is called the centripetal force FC.

6. Centripetal Acceleration

7. Vectors in Uniform Circular MotionvT vT ac ac vT ac vT ac

8. Centripetal Acceleration aC
Centripetal acceleration is often called radial acceleration because it is directed along the radius toward the center of the circular path.

9. Tangential and Centripetal Acceleration
Tangential aT and centripetal aC acceleration are perpendicular to each other.
Tangential acceleration aT is a result of a change in speed.
Centripetal acceleration aC is a result of a change in direction.

10. Tangential and Centripetal Acceleration

11. Centripetal Force
Centripetal force is the force that maintains circular motion.
Inertia tends to maintain the tangential component of motion and the force directed toward the center of the circle counters the inertia and maintains the circular motion.

12. Centripetal Force
When the centripetal force is removed, the object does not continue to move in a circle. The object will move in a straight line that is tangent to the point at which the force stopped.