dynamics of circular motion 14154
DESCRIPTION
LectureTRANSCRIPT
Dynamics of Circular Motion
Types of Circular MotionCentripetal ForceCentripetal AccelerationHorizontal CircleVertical CircleBanking of CurvesConical Pendulum
CIRCULAR MOTION- Motion of a body in a curved path
TYPES: Uniform Circular Motion, UCM – motion with
constant speed Ex. A car rounding an oval at 30 KPH
Non-Uniform circular Motion, NUCM – a roller coaster car that slows down and speeds up as it moves around a vertical loop.
V
VS
r
Conversion:1 rev = 360° = 2π rad
c
In uniform circular motion, the speed is constant, but the direction of the velocity vector is not constant.
90
90
Centripetal Acceleration
rtv
vv
rv
tv 2
rvac2
S
Concept in Uniform Circular Motion
Period & Frequency
Period, T - time it takes for the object to travel once around the circle. (sec)
Frequency, f – no. of cycles or no. of revolutions that the
body makes in 1 sec (rev/sec, cycles/sec, hertz)
vr
T2
r 𝑻 = 1/𝒇
Centripetal Force
Thus, in uniform circular motion there must be a netforce to produce the centripetal acceleration.
The centripetal force is the name given to the net force required to keep an object moving on a circular path.
The direction of the centripetal force always points towardthe center of the circle and continually changes direction as the object moves.
rvmmaF cc
2
Unbanked Curves
On an unbanked curve, the static frictional forceprovides the centripetal force.
Car Rounding a Flat Curve at Constant Speed
Banked Curves
On a frictionless banked curve, the centripetal force is the horizontal component of the normal force. The vertical component of the normal force balances the car’s weight.
Banked Curves ( Neglecting Friction)
rvmnFc2
sin
mgn cos rgv2tan
nn cos θ
Summary
rectilinear
Summary
Sample Problems1.
3.
2.
Sample Problems
5.
4.
vertical.
6. The 4-kg in the figure is attached to a vertical rod by means of two strings. When the system rotates about the axis of the rod, the strings are extended as shown and the tension in the upper string is 80 N.
a) What is the tension in the lower cord?
b) b) How many revolutions per minute does the system make?