# Circular Motion

Circular Motion vt ac The basics 1 Rev = 1 revolution

To go around a circle once T is the Period (measured in seconds) Time it takes to complete 1 rev is the frequency (measured in Hz = 1/sec) =1/T

RPS = Revolutions per second RPM = Revolutions per minute For UCM problems, we can use rps as the frequency MBQ What is 60.0 rpm in rps?

1 rps Uniform Circular Motion When an object moves in a circle, its velocity is continuously changing direction The direction of the objects velocity is tangent to the circle

The magnitude of the velocity is called tangential speed, vt The t in vt is a subscript ( we are not multiplying by t) Uniform Circular Motion (UCM) is circular motion at constant speed vt is constant

Tangential Speed Angular Speed = v/r Angular speed is measured in radians per

second (rad/s) It is a measurement of the change in angle per time Centripetal Acceleration Anything moving in a circle is accelerating, since 1. Acceleration is a change in velocity with time

2. The direction of the objects velocity is continuously changing The acceleration due to the continuously changing direction is called centripetal acceleration, ac ac points towards the center of the circle and is perpendicular to velocity

=

Example A building superintendent twirls a set of keys in a circle at the end of a cord. If the keys have a centripetal acceleration of 145 m/s2 and the cord has a length of 0.34m, what is the tangential speed of the keys?

7.0 m/s Centripetal Force The net force acting on an object points in the same direction as its acceleration Fnet = ma, so Centripetal force, Fc, is the net force acting on

an object moving in UCM Direction of Fc is toward center of circle Fc acts perpendicular to objects motion Example A 5.00 kg mass is swung in a vertical circle of radius 0.400 m. It is attached to a string

that can take 125 N of tension before breaking. What is the maximum speed of the mass? 2.47 m/s Example

Which of the following describes a car traveling on a flat road in uniform circular motion?

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