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+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.
+Centripetal Acceleration ! Vector
! Always perpendicular to the path of the motion.
! Points toward the center of the circle.
2
Cvar
=
+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
+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
+ When Acceleration is not uniform -Tangential Acceleration exists
! When v varies.
! Motion is not uniform circular motion.
+Total Acceleration
! Tangential acceleration:
! Radial acceleration:
! Total acceleration:
td
adt
=v
2
r Cva ar
= − = −
2 2r ta a a= +
+Example 2
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
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