dynamics of circular motion 14154

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?