1

Click anywhere in the Click anywhere in the black area black area below to see a movie.below to see a movie.

A

B

C

A ball is going around in a circle attached to a string. If the string breaks at the instant shown, which path will the ball follow? 2

A

B

C

A planet is going in a circular orbit around a star. If the star was to suddenly disappear at the instant shown, which path will the planet follow?

2

A

B

C

A ball is going around in a horizontal circle on a frictionless table attached to a string. If the string breaks at the instant shown, which path will the ball follow?

2

Uniform Circular motion

Uniform circular motion in a horizontal plane

v

mg

N

Tr

m

mw

N = mg

Net force = T

F = maT = m (v2 / r)

T = mwg as it is at rest.mwg = m v2 / r

mw= mass (downward)

Uniform Circular motion

Uniform circular motion in a horizontal plane

v

mg

N

Tr

m

mw

T = m (v2 / r)

What is the physical meaning of the formula?(1) What happens if the initial speed v of the bob is forced to move faster? A greater T is needed, the greater mw, to keep the radius of motion r.

It will slide out to attain a greater r.

(2) What happens if there is energy lost due to friction on the plane? v decreases By T = mv2 / r, r decreases(3) What happen if an additional mass is added to the weight mw? M moves down r decreases and T increases v increases

Uniform Circular motion

Uniform circular motion in a horizontal plane

v

mg

N

Tr

m

M

T = m (v2 / r)

What is the physical meaning of the formula?

(4) What happens if the string suddenly break? • Tension suddenly disappears and there is no more centripetal force.• No more circular motion can be maintained.• The bob will move with its velocity tangent to the circle

at the instant the string breaks

When we see an object carrying out circular motion, we know that there must be force acting on the object, directed towards the center of the circle.

When you look at the circular motion of a ball attached to a string, the force is provided by the tension in the string.

When the force responsible for the circular motion disappears, e.g. by cutting the string, the motion will become linear.

In most cases, the string force not only has to provide the force required for circular motion, but also the force required to balance the gravitational force.

Important consequences: You can never swing an object

with the string aligned with the horizontal plane.

When the speed increases, the acceleration increases up to the point that the force required for circular motion exceeds the maximum force that can be provided by the string.

When you drive your car around a corner you carry out circular motion.

In order to be able to carry out this type of motion, there must be a force present that provides the required acceleration towards the center of the circle.

This required force is provided by the friction force between the tires and the road.

But remember ….. The friction force has a maximum value, and there is a maximum speed with which you can make the turn.

Required force = Mv2/r.If v increases, the friction force must increase and/or the radius must increase.

You are driving a car with constant speed around a horizontal circular track.

Normal

On a piece of paper, draw a Free Body Diagram (FBD) for the car. On a piece of paper, draw a Free Body Diagram (FBD) for the car.

How many forces are acting on the car?How many forces are acting on the car? A) 1 B) 2 C) 3 D) 4 E) 5

25

The net force on the car isThe net force on the car is

A. Zero A. Zero B. Pointing radially inward (centripetal!)B. Pointing radially inward (centripetal!)C. Pointing radially outwardC. Pointing radially outward (centrifugal?)(centrifugal?)

Gravity

Friction

Davain sits on the outer rim of a merry-go-round, and Diego sits midway between the center and the rim. The merry-go-round makes one complete revolution every two seconds.◦ Diego’s angular velocity is:

(a)(a) the same as Davian’s

(b)(b) twice Davian’s

(c)(c) half Davian’s

Diego Davian

Uniform Circular Motion◦ Speed is constant◦ Direction is changing◦ Acceleration toward center a = v2 / r◦ Newton’s Second Law F = ma

http://www.physicsclassroom.com/

How does this apply to planets?

http://hyperphysics.phy-astr.gsu.edu/hbase/hframe.html

Check out this Check out this tutorial!tutorial!

Click on this Click on this question to question to investigate!investigate!

Are you Are you HYPERHYPER enough to learn enough to learn and link?and link?

http://www.animations.physics.unsw.edu.au/mechanics/chapter3_circularmotion.html

Check out this site for simulations of circular Check out this site for simulations of circular motionmotionAnd so many other simulations!And so many other simulations!

CitationsCitations

Graphics: Slides 9, 10, 11Physics Text 1 Chapter 3 Vectors and Two-Dimensional Motion

Slides 12, 13Physics Text 2

Video:Planetary Orbits are Elliptical. Discovery Channel School. 2005.Discovery Education. 17 July 2009http://streaming.discoveryeducation.com/

Websites:http://hyperphysics.phy-astr.gsu.edu/hbase/orbv.html#co

http://www.physicsclassroom.com/

http://hyperphysics.phy-astr.gsu.edu/hbase/hframe.html

http://www.animations.physics.unsw.edu.au/mechanics/chapter3_circularmotion.html