SIMPLE HARMONIC MOTION

SIMPLE HARMONIC MOTION

1. 1. Understand how all objects which change directions must be accelerating, even at constant speed. You must apply this knowledge to explain why all changes in direction must involve a centripetal force

   • i. Velocity is a vector (it has both magnitude and direction)
     • ii. As the object travels around a circle, it changes direction
       • iii. If a car is going at a constant speed, its velocity is changing because its direction is changing.
         • iv. acceleration is the rate of change in velocty
           • v. Therefore acceleration is present (even its not going any faster0
             • VI. There must be an resultant unblaanced froce acting to cause the acceleration (F=MA)
               • vii. This force is known as centripetal force and is directed towards the centre of the cirular motion
                 • People in the London eye may not notice they are being accelerated but if the wheel is rotated at a bigger speed than usual, they certainly would

2. 2. You must know the relationship between velocity and centipetal force and be able to state the work done by centripetal foce

   • Velcoity is tangential to acceleration that is directed towards the center of the circle
     • the centripetal force (acceleration) is always right angle to the velocity, otherwise the speed would increase (velocity magnitude stays the same, only direction is changing)
       • the force acting perpendicular to velocity of an object result in circular motion

3. 3. State the work done by centripetal force

   • This would mean that the force is directed perpendicular to the direction that the object is being displaced. The angle theta in above equation is90 degrees ad the cosine of 90 degrees is 0. Thus the work done by the centripetal force in the case of uniform circular motion is 0 joules.
     • EXAMPLE: The moon orbits around the earth may be assumed to be circular. Explain why no work is done by the gravitational force that acts on the Moon to keep it in around the Earth
       • Work done is Force x distance int eh direction of the force
         • Think about the direction in which the force is acting, and the thik about the direction in which the moon is moving at any instant in time

4. 5. Be able to relate angular velocity to period of rotation and frequency

   • THE FREQUENCY; is the number of revolutions the body will complete in one second
     • THE TIME PERIOD: is the time taken, in seconds, it takes for the body to complete one revolution
   • ANGULAR SPEED:(W) is defined as the angle turned per unit time. Its unit is in radians per second (Rad -1) .
     • for a complete circle, an object turns through 2 in a time(T), so frequency and period are related to omega (W0 by