Transcript Uniform Circular Motion - Tenafly Public Schools

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
2
v
aC 
r
• Always perpendicular to the path of
the motion.
• Points toward the center of the
circle.
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 period
f= 1
T
Tangential Speed in terms
of T or f
v=2pr/T
v=2prf
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)
Total Acceleration
• Tangential acceleration:
• Radial acceleration:
• Total acceleration:
2
v
ar  aC  
r
a  a a
2
r
d v
at 
dt
2
t
Total Acceleration
2
dv ˆ v
a  at  a r 
q  rˆ
dt
r
– r, radius vector
 q , tangent to the
circle
Example 2 (#34)
An automobile whose speed is
increasing at a rate of 0.6m/s2 travels on
a circular road of radius 20m. When the
instantaneous speed of the car is 4m/s
find: a)the tangential acceleration, b)the
centripetal acceleration, c)the magnitude
and direction of the total acceleration.
Ans: a)0.6m/s2,b)0.8m/s2, c)1m/s2,53.1o