Circular Motion Chapter 12

Measuring the size of an angle In everyday life angles are measured in a unit called the degree. 1 degree = 1o = of a full circle

The Radian Another Unit used to measure angle is the radian. One radian is the angle at the centre of a circle subtended by an arc, which is equal in length to the radius of the circle.

In the diagram: The arc length s = 200 m The radius r = 75 m The angle  in radians is:

π radians 180o =  radians i.e. 180o = 3.14159 rad Using this formula you can convert degrees to radians or radians to degrees. π radians

What is Angular Velocity? Angular Velocity (ω) is the rate of change of angle with respect to time. Where ω is angular velocity  is the angle traced out and t is the time taken.

Angular Velocity P moves around the circle with a steady linear speed v. As P moves the angle  changes. ANGULAR VELOCITY The rate at which the angle  is changing with respect to time is called the angular velocity of P about O.

What is the SI Unit of Angular Velocity? The SI Unit of angular Velocity is the radian per second (rad​ s​-1​) Angular Velocity is a Scalar Quantity..

An object moving in a circle at a steady speed traces out an angle of 10 radians in 4 seconds. Find its angular velocity.

Relationship between Linear Velocity v and Angular Velocity ω. A disc rotates with constant angular velocity ω about its centre. The greater the distance a particle on the disc is from the centre, the greater its linear velocity v.

What is the relationship between Linear Velocity v and Angular Velocity ω ? v = r ω Linear velocity = Angular velocity × Radius

What is Centripetal Force? If a body is moving in a circle the force towards the centre needed to keep it moving in that circle is called Centripetal Force.

A body of mass m is moving with a speed v and angular velocity ω in a circular path of radius r. Write down a formula for the Centripetal Force acting on it OR

What is Centripetal Acceleration? If a body is moving in a circle the acceleration it has towards the centre of that circle is called Centripetal Acceleration.

Newton’s Law of Universal Gravitation states that any two point masses in the universe attract each other with a force that is: directly proportional to the product of their masses and inversely proportional to the square of the distance between them.

Write down a mathematical expression for Newton’s Law of Universal Gravitation.

The force of gravity provides the centripetal force needed to keep the planets in orbit around the Sun. Note: Pluto has been reclassified as a dwarf planet.

A satellite orbits a planet. What is meant by the Period of its Orbit? The Period of its Orbit is the time taken for the satellite to go once around the planet.

A satellite orbits a central body A satellite orbits a central body. What is the relationship between the period T, the speed of the satellite v and the radius of the orbit R?

A satellite orbits a central body. What is the relationship between the period, the mass of the central body and the radius of the orbit? T  =  period of orbit; R = radius of its orbit; G = gravitational constant M = mass of central body.

If a satellite orbits in the equatorial plane; If its period is 24 hours; If the satellite moves in same direction as Earth rotates, then: The orbit is Geostationary.