1. What is Circular Motion?

2. Uniform Circular Motion
Motion of an object travelling at constant speed in a circle
Let’s explore the kinematics of circular motion.
Why is it accelerating, if the speed is constant?
What would cause an object to move in a circle?

3. What is Centripetal Force?
Objects move in a straight line at a constant speed unless a force acts on them. This is Newton's First Law.
However, many things move in curved paths, especially circles, and so there must be a force acting
on them to pull them out
of their straight line paths
and make them turn
corners.

4. What Does Centripetal Force Depend On?
We call the force that makes objects move in a circle the CENTRIPETAL FORCE(the name comes from Latin and means centre-seeking)
How is Centripetal Force related to:
Mass of object?
Velocity of object?
Radius size of circle?
Let’s Explore!

5. Uniform circular motion
The speed stays constant, but the direction changes v R
The acceleration in this case is called
centripetal acceleration

6. Wide turns and tight turns
little R
big R
for the same speed, the tighter turn requires more
acceleration

7. Let’s Determine the Velocity of an Object Travelling in a Circle…
Remember: Speed = Distance/Time
Let’s define Period (T) as the time it takes the object to travel once around the circle.
How far does it travel in one rotation?
Therefore:

8. path of ball if the string
Ball on a string
The tension in the string
provides the necessary
centripetal force to keep
the ball going in a circle.
path of ball if the string
breaks

9. Example
What is the tension in a string used to twirl a 0.3 kg ball at a speed of 2 m/s in a circle of 1 meter radius?
Force = mass x acceleration [ m  aC ]
acceleration aC = v2 / R = (2 m/s)2/ 1 m
= 4 m/s2
force = m aC = 0.3  4 = 1.2 N
If the string is not strong enough to handle this tension it will break and the ball goes off in a straight line.

10. Motion On A Flat Curve
On a flat, level curve, the friction between the tires and the road supplies the centripetal force.
If the tires are worn smooth or the road is icy or oily, this friction force will not be available.
The car will not be able to move in a circle, it will keep going in a straight line and therefore go off the road.

11. What’s this Centrifugal force ? ?
The red object will make the turn only if there is enough friction on it
Otherwise it goes straight
The apparent outward force is called the centrifugal force
It is NOT A REAL force!
An object will not move in a circle until something makes it, in this case the car door!
object on
the dashboard
straight line
object naturally
follows

12. What is Gravitational Force?
Sir Isaac Newton discovered that every particle attracts every other particle in the universe with a force when he saw an apple fall from a tree towards the earth.
The force of attraction between any two particles in the universe is called Gravitation or gravitational force

13. Newton’s Law of Universal Gravitation
G is the universal gravitational constant and equals x Nm2 / kg2

14. G vs. g Always distinguish between G and g
G is the universal gravitational constant
It is the same everywhere
g is the acceleration due to gravity
g = 9.80 m/s2 at the surface of the Earth
g will vary by location

15. Why doesn’t the moon fall into the earth?
The moon is actually falling toward Earth but has great enough tangential velocity to avoid hitting Earth.
If the moon did not fall, it would follow a straight-line path.

16. Newton’s Hypothesis

17. Johannes Kepler 1571 – 1630 German astronomer
Best known for developing laws of planetary motion
Based on the observations of Tycho Brahe

18. Kepler’s Laws Kepler’s First Law Kepler’s Second Law
All planets move in elliptical orbits with the Sun at one focus
Kepler’s Second Law
The radius vector drawn from the Sun to a planet sweeps out equal areas in equal time intervals
Kepler’s Third Law
The square of the orbital period of any planet is proportional to the cube of the semimajor axis of the elliptical orbit

19. Kepler’s Third Law Can be predicted from the inverse square law
Start by assuming a circular orbit
The gravitational force supplies a centripetal force
Ks is a constant

20. Mass of the Sun
Using the distance between the Earth and the Sun, and the period of the Earth’s orbit, Kepler’s Third Law can be used to find the mass of the Sun
Similarly, the mass of any object being orbited can be found if you know information about objects orbiting it