Circular Motion AP Physics C Mrs Coyle Circular

Circular Motion AP Physics C Mrs. Coyle

Circular Motion • Uniform circular motion (constant centripetal acceleration) • Motion with a tangential and radial (centripetal)acceleration

Uniform Circular Motion • Object has a circular path, constant speed. • The velocity is always tangent to the path of the object.

Why is there acceleration in uniform circular motion? Dv = vf – vi a= Dv/ Dt

Centripetal Acceleration • Vector • Always perpendicular to the path of the motion. • Points toward the center of the circle.

Characteristics of Uniform. Circular Motion • Tangential (linear) Velocity • Frequency • Period • Centripetal Acceleration

Frequency, f : #revolutions per unit time • f = # rev / time Units: • (1/sec)=sec-1=Hertz (Hz) • rpm (#rev/min) • rps (#rev/sec) r

Period • Period T : time for 1 revolution – Unit: sec, min, h • Relating Frequency and period f= 1 T

Tangential Speed in terms of T or f v=2 pr/T v=2 prf

Example 1 • A boy whirls a stone in a horizontal circle of r=1. 5 m, 2 m above the ground. The string breaks and the stone strikes 10 m away. What was the centripetal acceleration during the circular motion? • Answer: 160 m/s 2

Tangential Acceleration • When v varies. • Motion is not uniform circular motion.

Total Acceleration • Tangential acceleration (vector) Plus • Radial acceleration (vector)

Total Acceleration • Tangential acceleration: • Radial acceleration: • Total acceleration:

Total Acceleration – r, radius vector - q , tangent to the circle

Example 2 (#34) An automobile whose speed is increasing at a rate of 0. 6 m/s 2 travels on a circular road of radius 20 m. When the instantaneous speed of the car is 4 m/s find: a)the tangential acceleration, b)the centripetal acceleration, c)the magnitude and direction of the total acceleration. Ans: a)0. 6 m/s 2, b)0. 8 m/s 2, c)1 m/s 2, 53. 1 o