Circular Motion

PhysicsMrs Coyle

•Earth rotates about its axis

•Satellite revolves about the earth

Part I-Intro to Circular Motion

Tangential Speed and Velocity Frequency and Period Centripetal Force Centripetal Acceleration

Characteristics of Circular Motion

Tangential (linear) Velocity Frequency Period

Frequency, f :#revolutions per unit time

f = # rev / time

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

r

Period

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

Relating Frequency and period f= 1

T

Arc Length

Arc Length s (unit: meter) Distance traveled along a circular

path.

s

Average Tangential (Linear) Speed

v= s t Unit: m/s

v= 2r/T = 2rf

Uniform Circular Motion

Linear(tangential speed is constant)

v=constant

Tangential (Linear) Velocity

v

v

The tangential velocity vector is tangent to the circle at the point of study.

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

Record Player

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

Merry-go-Round

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?

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?

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.

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.

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.

Centripetal Force

Fc=mac

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

Part II More Centripetal Force Problems

Car Rounding a Curve Loop-the- loop Rotor

What force plays the role of the centripetal force when a car rounds a curve?

Car Rounding a Bend

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

What force plays the role of the centripetal force when a ball is on the top of a loop-the-loop?

Loop the Loop

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

Rotor Ride

What force plays the role of the centripetal force in the rotor ride?

http://upload.wikimedia.org/wikipedia/commons/7/7d/Rotormidcyclelunapraksyd.JPG

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