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What is Circular Motion?

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?.

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What is Circular Motion?

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  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. 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. 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. Motion On A Flat Curve

  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 Gravitationorgravitational force

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

  14. G vs. g • Always distinguish between G and g • Gis the universal gravitational constant • It is the same everywhere • gis 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 • 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. 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 Kepler’s Third Law

  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

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