Rotational Motion

1. Rotational Motion

2. Uniform Circular Motion Using similar triangles abc def v1 Where r is proportional to v1or v2 f d 2 ac = Centripetal Acceleration 7v 7v Chord ab ---- = ------------- v r r v2 The direction of the centripetal acceleration is always toward the center of the circle Chord ab = d = v t 2 r e 7v v t ---- = ------------ a v r 7v Chord ab Since a = ------ t b 7v v x v ---- = ----------- t r v 2 ac = ----- r c

3. Difficult to directly measure velocity of an object moving in a circle. Useful to measure the “time for one complete revolution”. Defined as the Period (T). The distance traveled in a circle is the circumference 2 r of the circle.

4. Centripetal Acceleration Can now calculate the acceleration of an object moving in a circle knowing the Period and radius of the circle. ( )

5. Centripetal Force If an object is moving in a circular path, there must be a change in its velocity and hence an acceleration. If there is an acceleration, a force must be present to cause this acceleration. It also must be in the same direction.

6. Circular Motion Equations Period = The time for one revolution Sometimes useful to show the number of revolutions per time Known as frequency Frequency is the inverse of the Period Units are

7. Problem: A 75.0 kg person is attached to a pole by a 5.00 meter rope. He makes one revolution in 4.50 seconds. Find: The speed of the person His Acceleration The Force required to keep him on his path

8. Problem 2: A car approaches a level, circular curve with a radius of 45.0 m. If the concrete pavement is dry, with a coefficient of friction of 1.20 between the rubber and concrete, what is the maximum speed at which the car can negotiate the curve at a constant speed? The car will be in uniform circular motion on the curve, so there must be a centripetal force. This force is supplied by friction, so the maximum frictional force provides the centripetal (net) force when the car is at its maximum tangential speed.