Circular Motion

AP Physics C

Circular Motion

Uniform circular motion (constant centripetal acceleration)

Object has a circular path, constant speed.

The velocity is always tangent to the path of the object.

Characteristics of UniformCircular Motion

Tangential (linear) Velocity Centripetal Acceleration Frequency Period

Speed/Velocity in a CircleConsider an object moving in a circle around a specific origin. The DISTANCE the object covers in ONE REVOLUTION is called the CIRCUMFERENCE. The TIME that it takes to cover this distance is called the PERIOD.

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Speed is the MAGNITUDE of the velocity. And while the speed may be constant, the VELOCITY is NOT. Since velocity is a vector with BOTH magnitude AND direction, we see that the direction o the velocity is ALWAYS changing.

We call this velocity, TANGENTIAL velocity as its direction is draw TANGENT to the circle.

Why is there acceleration in uniform circular motion?

v = vf – vi

a= v/t

Centripetal Acceleration

metersin length arc

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Suppose we had a circle with angle, between 2 radaii. You may recall:

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Centripetal means “center seeking” so that means that the acceleration points towards the CENTER of the circle

Centripetal Acceleration

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Always perpendicular to the path of the motion.

Points toward the center of the circle.

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Drawing the Directions correctly

So for an object traveling in a counter-clockwise path. The velocity would be drawn TANGENT to the circle and the acceleration would be drawn TOWARDS the CENTER.

To find the MAGNITUDES of each we have:

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Frequency, f :#revolutions per unit time

f = # rev / time

Units: (1/sec)=sec-1=Hertz (Hz) rpm (#rev/min) rps (#rev/sec)

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Period

Period T : time for 1 revolution Unit: sec, min, h

Relating Frequency and periodf= 1

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Tangential Speed in Relation to Angular Speed Imagine you are at a rollerblading party.. You

play a game where you join hands in one long chain of people and then start going in a circle… where do you want to be? Who is moving faster?

- angular speed Units: radians/s; rpm (rev/min)

=/t v=r

Example 1

A boy whirls a stone in a horizontal circle of r=1.5m, 2m above the ground. The string breaks and the stone strikes 10m away. What was the centripetal acceleration during the circular motion?

Answer: 160m/s2

Examples

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The blade of a windshield wiper moves through an angle of 90 degrees in 0.28seconds. The tip of the blade moves on the arc of a circle that has a radius of 0.76m. What is the magnitude of the centripetal acceleration of the tip of the blade?

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Circular Motion and N.S.L

Recall that according to Newton’s Second Law, the acceleration is directly proportional to the Force. If this is true: ForcelCentripetaF

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Since the acceleration and the force are directly related, the force must ALSO point towards the center. This is called CENTRIPETAL FORCE.

NOTE: The centripetal force is a NET FORCE. It could be represented by one or more forces. So NEVER draw it in an F.B.D.

Examples

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What is the minimum coefficient of static friction necessary to allow a penny to rotate along a 33 1/3 rpm record (diameter= 0.300 m), whenthe penny is placed at the outer edge of the record?

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ExamplesThe maximum tension that a 0.50

m string can tolerate is 14 N. A 0.25-kg ball attached to this string is being whirled in a vertical circle. What is the maximum speed the ball can have (a) the top of the circle, (b)at the bottom of the circle?

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