1. Circular Motion By: Heather Britton

2. Circular Motion Uniform circular motion - the motion of an object traveling at constant speed along a circular path Period (T) - the time it takes to make one revolution

3. Circular Motion Circumference - 2πr Since velocity is expressed as a distance divided by time we can calculate the velocity of an object in uniform circular motion by v = (2πr) / T

4. Circular Motion Frequency - the number of cycles completed by a periodic quantity in a unit time Usually measured in cycles per second (s -1 ) Period and frequency are reciprocals of each other

5. Circular Motion Example 1: A tire balancing machine rotates at 830 rpm. If a wheel has a radius of 0.29 m, what is the speed of the outer edge?

6. Circular Motion The magnitude of the velocity may be constant, but the direction is always changing Therefore the object is experiencing constant acceleration

7. Circular Motion At t o our initial velocity vector is as follows: At t our velocity vector is as follows: Because it is a circle the radii are equal, so r o = r Because it is uniform circular motion the magnitude of v o = v

8. Circular Motion If we superimpose the circles and look at r o and r we can see the displacement = l Due to the right angles the velocity vectors will form a similar triangle if both v o and v start from a common origin The change in velocity is similar to l

9. Circular Motion Δv = (vl) / r From previous chapters we know that a = Δv / t So we will divide both sides by t l is a displacement so we can substitute l for x

10. Circular Motion a c = v 2 /r a c = centripetal acceleration (m/s 2 ) v = velocity (m/s) r = radius (m) The direction of the acceleration is always towards the center

11. Circular Motion Example 2: A bobsled track has turns with a radius of 33 m and 24 m. If the bobsled has a velocity of 34 m/s, what is the acceleration in terms of g’s for the two turns?