Circular Motion

AP Physics CMrs. 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?

v = vf – vi

a= v/t

Centripetal Acceleration• Vector

• Always perpendicular to the path of the motion.

• Points toward the center of the circle.

2

C

va

r

Characteristics of UniformCircular 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 periodf= 1

T

Tangential Speed in terms of T or f

v=2r/T

v=2rf

Example 1

• A boy whirls a stone in a horizontal circle of r=1.5m, 2m above the ground. The string breaks and the stone strikes 10m away. What was the centripetal acceleration during the circular motion?

• Answer: 160m/s2

Tangential Acceleration

• When v varies.

• Motion is not uniform circular motion.

Total Acceleration• Tangential

acceleration (vector)

Plus

• Radial acceleration (vector)

• Tangential acceleration:

• Radial acceleration:

• Total acceleration:

t

da

dt

v

2

r C

va a

r

2 2r ta a a

Total Acceleration

Total Acceleration

– r, radius vector , tangent to the circle

2ˆ ˆt r

d v

dt r

va a a r

Example 2 (#34)

An automobile whose speed isincreasing at a rate of 0.6m/s2 travels ona circular road of radius 20m. When theinstantaneous speed of the car is 4m/sfind: a)the tangential acceleration, b)thecentripetal acceleration, c)the magnitudeand direction of the total acceleration.

Ans: a)0.6m/s2,b)0.8m/s2, c)1m/s2,53.1o