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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
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linear velocity
- arc length per unit time
- instantaneous velocity of a body in circular motion
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v =
- s/t
- where v = linear velocity
- s = arc length
- t = time taken
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linear velocity is a ... quantity
vector
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the direction of one point in circular motion is
the tangent direction of the circumference at that point
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angular velocity/speed
in rotation the angle turned through per second , units radians per second , rad s-1
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one radian is defined as
the angle subtended at the center of a circle by an arc equal length to the radius
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if we let the arc length become the entire circumference then s =
2pir
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the angle in radians generated in going around a complete circle is
2pi
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the angular change in full rotation is
either 360 degrees or 2pi radians
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angular velocity symbol =
w
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time period =
the time a body in circular motion takes to complete one revolution , symbol T , units seconds s
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frequency
- the number of revolutions per second , symbol f , units hertz , Hz ,
- the reciprocal of time period
- T = 1/f
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rotational speed =
angular speed/velocity
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if a body is in uniform circular motion along a circumference of radius r the arc it covers in a period T is
2pir
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hence the linear velocity , v , =
2pir/T
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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
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the magnitude of the centripetal force =
mv2/r
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the magnitude of the centripetal force is .... throughout motion
constant
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the centripetal force always points
towards the center of the circle and continually changes direction as the object moves
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by newtons second law F = ma
- 4pi2mr/T2 = ma
- 4pi2r/T2 = a
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the centripetal acceleration vector always points
towards the center and continually changes direction as the object moves
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s , displacement =
a vector describing the difference in position of two points
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sometimes the displacement may be
2r (see diagram in notes to know when this applies)
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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
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for a particle moving with uniform speed the kinetic energy of the particle is
constant
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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
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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
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the aircraft is banked
the horizontal component of the support force is acting as the centripetal force
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what produces the force necessary to accelerate pilot
reaction with seat/friction between passenger and seat
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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
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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
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angular displacement =
- angle turned through in a given time
- 2pit/T
- 2pift
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angular speed/velocity =
angular displacement per second
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centripetal force for a car going round a roundabout
friction
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centripetal force for ball on a string
tension in string
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centripetal force for earth moving round sun
gravity
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see diagram in notes hard to explain
:)
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banking reduces centripetal force because
the horizontal component is reduced
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15m from axis of rotation means
15m is the radius
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for a particle moving in a circle with uniform speed there's sometimes displacement of the particle in the
direction of the force
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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
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for a particle moving in a circle with uniform speed the kinetic energy of the particle is
constant
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