circular motion
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Circular Motion
PhysicsMrs Coyle
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•Earth rotates about its axis
•Satellite revolves about the earth
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Part I-Intro to Circular Motion
Tangential Speed and Velocity Frequency and Period Centripetal Force Centripetal Acceleration
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Characteristics of Circular Motion
Tangential (linear) Velocity Frequency Period
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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)
r
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Period
Period T : time for 1 revolution Unit: sec, min, h
Relating Frequency and period f= 1
T
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Arc Length
Arc Length s (unit: meter) Distance traveled along a circular
path.
s
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Average Tangential (Linear) Speed
v= s t Unit: m/s
v= 2r/T = 2rf
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Uniform Circular Motion
Linear(tangential speed is constant)
v=constant
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Tangential (Linear) Velocity
v
v
The tangential velocity vector is tangent to the circle at the point of study.
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Problem 1A biker travels once around a circulartrack of radius 20.0m in 3s. Calculate:a) the average tangential speedb) the frequencyc) the period
Answers: 41.9m/s, f=0.33Hz, T=3s
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Record Player
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Problem 2
A coin sits 0.10m from the center of arecord player spinning at 45rpm.a) What is the frequency in Hertz?b) What is the period?c) What is the linear speed?
Answer: 0.75Hz, 1.33s, 0.47m/s
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Merry-go-Round
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How does the v vary with r?
The linear speed increases as r increases.
Example: How does your linear speed change
when you are on a merry-go-round and you move away from the center?
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How does the f vary with r?
f does not depend on r
Example: How does your frequency change
when you are on a merry-go-round and you move away from the center?
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Centripetal Force, Fc= m v2
r
Is a center seeking force. (Always points to the center.)
Is perpendicular to the tangential velocity at any given instant.
It is not an extra force. An existing force represents the centripetal force.
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What forces represent the centripetal force in these examples?
Car on bend of road. Coin on record player. Child on merry-go-round. Ball tied on a string.
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Centripetal Acceleration, ac= v2
r
Has same direction as centripetal force.(Always points to the center).
Is perpendicular to the tangential velocity at any given instant.
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Centripetal Force
Fc=mac
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Problem 3
A child on a merry-go-round sits 1.5mfrom the center. They spin 3 times in onemin. The mass of the child is 40kg.Find the friction(centripetal force) acting onthe child.
Answer: 5.9N
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Part II More Centripetal Force Problems
Car Rounding a Curve Loop-the- loop Rotor
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What force plays the role of the centripetal force when a car rounds a curve?
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Car Rounding a Bend
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Example 1: Car Rounding a Curve
A car is travelling with a speed of 45km/h on a circular horizontal track of radius 50m. What is the minimum coefficient of friction, so that the car stays on the track?
Answer: 0.3
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What force plays the role of the centripetal force when a ball is on the top of a loop-the-loop?
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Loop the Loop
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Example 2: Loop-the-loop What is the critical velocity of a ball
at the top of the loop of radius .3m so that it completes the loop?
Answer: 1.7m/s
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Rotor Ride
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What force plays the role of the centripetal force in the rotor ride?
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Example 3: Rotor
A brave student rides in a rotor of radius 5m whose floor drops when it reaches a speed of 20mi/h. What is the coefficient of friction between the student and the wall of the rotor, so that the student does not fall?
Answer: 0.6