What is Circular Motion?

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?

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.

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!

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

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

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:

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

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.

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.

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

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

Newton’s Law of Universal Gravitation G is the universal gravitational constant and equals 6.673 x 10-11 Nm2 / kg2

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

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.

Newton’s Hypothesis

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

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

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

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