Circular Motion Unit 5 http://www.youtube.com/watch?v=-G7tjiMNVlc http://www.youtube.com/watch?v=L6-kn2tB-9E http://www.youtube.com/watch?v=ITA1rW5UraU http://www.youtube.com/watch?v=z3BSkMj1wLc

What is “circular motion”? An object that moves in a circular path about an external point is in circular motion.

Rotation v. Revolution Rotation – When an object turns about an internal axis. Ex. Earth rotates on an axis passing through it’s geographical poles every 24 hrs. Revolution – When an object turns on an external axis. Ex. Earth revolves around the sun every 365.25 days.

Period vs. Frequency Period ( T ) – time it takes for one full rotation or revolution Measured in seconds Frequency ( f ) – number of rotations in one sec Measured in Hertz (Hz) Which is an inverse sec

Example 1

Arc Length Refers to the length, in meters, that an object travels along the circumference of a circle. The symbol for arc length is s s

Angle Arc length depends on the radius. Any point on the radius will have the same angular displacement. Angle in this case is measured in radians and NOT degrees. s r θ

Angular vs. Linear Velocity Angular velocity (w) Speed object travels while in circular motion Does NOT depend on radius Units rotations/sec OR revolutions/sec Tangential (linear) velocity Speed object travels when released from circle Travels in a straight path tangent to the circle Depends on length of radius m/s

The Value of VT The tangential speed depends on the size of the path’s radius. As radius decreases, vT increases

Example 2

The Change in vT Velocity Speed – constant in circular path Direction-changes direction So…..velocity changes which is the definition of acceleration Acceleration Centripetal acceleration (ac) Direction of ac is towards the center

Example 3

Centripetal Force For circular motion, the net force influencing acceleration is called a centripetal force. Force that keeps an object going in a circular path. This force is directed toward the center of rotation or center of a curvature.

Centripetal Force If there was no centripetal force, what would be the direction of the occupants of a merry-go-round? They would continue on a straight line due to the object’s inertia and maintain their instantaneous tangential velocity.

Ball on a String Example Inertia maintains ball’s motion in a linear path Tension on the string is an applied net external force directed toward the center of rotation Causes a constant change in velocity, making the ball follow a circular path

Centripetal Force Using Newton’s Second Law equation (Fnet = ma),

Example 4