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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