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if a particle , moving along a circle passes an equal arc length in equal time , this is called
uniform circular motion

linear velocity
 arc length per unit time
 instantaneous velocity of a body in circular motion

v =
 s/t
 where v = linear velocity
 s = arc length
 t = time taken

linear velocity is a ... quantity
vector

the direction of one point in circular motion is
the tangent direction of the circumference at that point

angular velocity/speed
in rotation the angle turned through per second , units radians per second , rad s^{1}


one radian is defined as
the angle subtended at the center of a circle by an arc equal length to the radius

if we let the arc length become the entire circumference then s =
2pir

the angle in radians generated in going around a complete circle is
2pi

the angular change in full rotation is
either 360 degrees or 2pi radians




angular velocity symbol =
w


time period =
the time a body in circular motion takes to complete one revolution , symbol T , units seconds s

frequency
 the number of revolutions per second , symbol f , units hertz , Hz ,
 the reciprocal of time period
 T = 1/f

rotational speed =
angular speed/velocity

if a body is in uniform circular motion along a circumference of radius r the arc it covers in a period T is
2pir

hence the linear velocity , v , =
2pir/T




the centripetal force is the
resultant force required to keep an object of mass , m , moving at speed , v , on a circular path of radius r

the magnitude of the centripetal force =
mv^{2}/r

the magnitude of the centripetal force is .... throughout motion
constant

the centripetal force always points
towards the center of the circle and continually changes direction as the object moves


from w = 2pi/T
F =
 mr(2pi/T)^{2}
 F = 4pi^{2}mr/T^{2}

by newtons second law F = ma
 4pi^{2}mr/T^{2} = ma
 4pi^{2}r/T^{2 }= a

the centripetal acceleration vector always points
towards the center and continually changes direction as the object moves

s , displacement =
a vector describing the difference in position of two points

sometimes the displacement may be
2r (see diagram in notes to know when this applies)

a mass on the end of a string is whirled round in a horizontal circle at increasing speed until the string breaks . the subsequent path taken by the mass is a
parabola in a vertical plane

for a particle moving with uniform speed the kinetic energy of the particle is
constant


if a wheel exceeds maximum rate of rotation the direction of motion of the particle immediately after it leaves the wheel will be at a
tangent


Figure 4 shows an aircraft which is flying in a horizontal circular path at constant speed (see notes , remember diagram ?) the aircraft has constant speed but not constant velocity explain why
 velocity is a vector quantity  direction of motion is continually changing
 speed is a scalar quantity  magnitude of motion is constant

the aircraft is banked
the horizontal component of the support force is acting as the centripetal force

what produces the force necessary to accelerate pilot
reaction with seat/friction between passenger and seat

forces when a mass is whirled in a circle in a vertical plane
tension at different points
 (see notes remember diagram ? )
 tension at the top is lowest
 tension at the bottom is highest
 top F = tension + mg
 bottom F = tension  mg

1 Figure 1 shows a space station that simulates gravity (artificial gravity). The station is designed in the shape of a cylinder which rotates about its long axis. (remember diagram)
artificial gravity appears to act .....
centripetal force acts ........
astronaut experiences .......
 outwards from the center towards the wall
 inwards on astronaut
 a reaction force of feet

angular displacement =
 angle turned through in a given time
 2pit/T
 2pift

angular speed/velocity =
angular displacement per second

centripetal force for a car going round a roundabout
friction

centripetal force for ball on a string
tension in string

centripetal force for earth moving round sun
gravity

see diagram in notes hard to explain
:)

banking reduces centripetal force because
the horizontal component is reduced

15m from axis of rotation means
15m is the radius

for a particle moving in a circle with uniform speed there's sometimes displacement of the particle in the
direction of the force

for a particle moving in a circle with uniform speed the force on the particle has constant magnitude and is always
perpendicular to the velocity of the particle

for a particle moving in a circle with uniform speed the kinetic energy of the particle is
constant

