1. Circular Motion Objectives Students should be able to: (a) define the radian; (b) convert angles from degrees into radians and vice versa;

2. Outcomes All should Be able to define the radian. Be able to convert degrees into radians and vice-versa. Most Should Be able to understand the reasons for using radians. Be able to solve problems involving a mixture of degrees and radians. Some Could Be able to explain what the idea of centrifugal force is and why it is imaginary. Be able to derive the equations for circular speed and centripetal acceleration.

3. Rotational Kinematics How do we describe an object moving in a circle?

4. Centripetal Force A circle follows a curve all the way round and we can describe it quantitatively as well as qualitatively. All objects that follow a curved path must have force acting towards the centre of that curve. We call this force the centripetal force. (Greek: Centre seeking).

5. Centripetal acceleration Since velocity is speed in a given direction if an object is travelling at a constant speed but is constantly changing direction it must be accelerating. This is what is happening in circular motion. The acceleration is called Centripetal Acceleration.

6. Dynamics of Rotation Examine circular motion taking Newton’s Laws into consideration. 1 st Law- 2 nd Law- 3 rd Law-

7. Dynamics of Rotation 1 st Law Is Moon at rest? Is Moon moving in a straight line? Conclusion MOON EARTH

8. Dynamics of Rotation 1 st Law Objects executing circular motion have a net force acting on them…even if you can’t see the agent of the force. What force acts on the Moon? MOON EARTH

9. Earth and Moon orbit the centre of mass of the system. Located 1070 miles below the Earth’s surface or 2880 miles from centre of Earth.

10. Circular velocity The instantaneous linear velocity at a point in the circle is usually given the letter v and measured in metres per second (m s -1 ). Speed is defined as the distance / time. For a circle, 1 complete circumference is 2  r and T is the Time period for one rotation (T) So v = 2  r / T

11. a = v 2 /r a is the Centripetal Acceleration. The change in velocity. O P Q v v 

12. Outcomes All should Be able to define the radian. Be able to convert degrees into radians and vice-versa. Most Should Be able to understand the reasons for using radians. Be able to solve problems involving a mixture of degrees and radians. Some Could Be able to explain what the idea of centrifugal force is and why it is imaginary. Be able to derive the equations for circular speed and centripetal acceleration.