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?

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.

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!

R v

The speed stays constant, but the direction changes

The acceleration in this case is called

centripetal acceleration

big R

little R

for the same speed, the tighter turn

requires moreacceleration

2

C

va =

R

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:

The tension in the stringprovides the necessarycentripetal force to keep the ball going in a circle.

path of ball if the stringbreaks

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.

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.

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 onthe dashboard

straight lineobject

naturallyfollows

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

G is the universal gravitational constant and equals 6.673 x 10-11 Nm2 / kg2

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

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.

1571 – 1630 German astronomer Best known for

developing laws of planetary motion• Based on the

observations of Tycho Brahe

Kepler’s First 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

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

2Sun Planet Planet

2

22 3 3

Sun

2

4S

GM M M v

r rr

vT

T r K rGM

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

2 3

Sun 2

4 rM

GT