Circular Motion Chapter 7 Section 1

What are we discussing today? Circular motion Centripetal acceleration & Centripetal force Tangential Speed You will calculate: ( 2 new calculations!) Tangential speed Centripetal acceleration Centripetal Force

Circular Motion Any object that is rotating about a single axis undergoes circular motion. The line about which the rotation occurs is called the axis of rotation.

Tangential Speeds Tangential speed (V t ) : the speed of an object along an imaginary line drawn tangent to the object’s circular path When tangential speed is constant, the motion is described as uniform circular motion Tangential speed depends on the distance from the object to the center of the circular path Example: Think about two horses side by side on a carousel. Each completes one full circle in the same time period. However, the horse on the outside covers more distance than the inside horse and thus has a greater tangential speed.

Centripetal Acceleration Even though tangential speed is constant, the object still has an acceleration Acceleration depends on a change in velocity. Velocity is a vector and thus has a magnitude and a direction. If the speed is constant then the direction must change in order for acceleration to occur. Objects traveling in a circle are CONSTANTLY changing direction and thus are constantly accelerating.

Centripetal Acceleration Centripetal acceleration: the acceleration directed toward the center of a curved path

Practice Problem

Tangential Acceleration Acceleration is due to either a change in speed or a change in direction Tangential acceleration is due to a change in speed Centripetal acceleration is due to a change in direction

Centripetal Force The net force directed toward the center of an object’s circular path is called centripetal force. Newton’s 2 nd Law can be used to find the magnitude of this force: F c = ma c

Centripetal Force Combining the equation for centripetal acceleration with Newton’s 2 nd law gives you the equation for centripetal force:

Practice Problem

F c necessary for circular motion Without centripetal force the object stops moving in a circular path and instead moves along a straight path that is tangent to the circle A) the string breaks and the ball moves vertically upward B) the string breaks at the top of the circular path and the ball flies off in the direction tangent to the path. The ball then moves in the parabolic path of the projectile.

Describing a Rotating System Centripetal force is the force that is directed inward toward the axis Centrifugal force is known as the force that pushes the passenger outward Inertia is often misinterpreted as a force.

Wrap Up What is tangential speed? What are the directions for the following: Centripetal acceleration Centripetal force Tangential speed