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define angular speed
- the angle turned through per second when an object is in rotation
- unit radians per second
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centripetal acceleration
an acceleration towards the center of a circular path
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centripetal force
- a force causing an object to move in a circular path ; it acts towards the center
- units Newtons
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frequency
- the number of oscillations or waves per second
- units hertz
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period
the time taken for one complete oscillation or one full rotation
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uniform circular motion
when an object rotates at a steady (constant) rate
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angular displacement
- the angle turned through in a given time when an object is in rotation
- units radians
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circumference of the wheel
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frequency of rotation
f = 1/T where T is the time for one rotation
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speed at any point on the perimeter
- 2 pi r / T
- r is in meters
- T is in seconds
- and the speed is in m/s
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angular displacement (radians) =
- 2 pi t / T
- where t = duration and T = time for one rotation
2 pi f
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in time , t , an object in uniform circular motion at speed v moves along the arc of the circle through a distance (in meters) :
- s = vt
- where s = distance , v=speed and t=time
- s = 2 pi r t / T
- s = θr
- s = wrt
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angular speed (rad/s) =
2 pi rpm/60
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rpm means
revolution per minute
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to convert from degrees to radians
/18/pi
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to convert from radians to degrees
x 180/pi
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the velocity of an object in uniform circular motion isn't constant because
the direction is continually changing , because velocity changes the object must accelerate
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the velocity of an object in uniform circular motion at any point is
along the tangent to the curve at that point
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to make an object move round on a circular path , it must
be acted on by a resultant force which changes its direction of motion
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the resultant force on an object moving round a circle at constant speed is called
centripetal force because it acts in the same direction as the centripetal acceleration which is towards the center of the circle
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for an object whirling round on the end of a spring , the .... is the centripetal force
tension in the string
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for a satellite moving round the earth .... is the centripetal force
gravity
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for a capsule on the london eye , the centripetal force is the
resultant force of the support force on the capsule and the force of gravity on it
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any object that moves in circular motion is acted on by
a resultant force which always acts towards the center of the circle . the resultant force is the centripetal force and therefor causes centripetal acceleration
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for a car travelling on the top op a hill
the support force from the road on the vehicle is directly upwards in the opposite direction to weight
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the resultant force is
s-mg
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the resultant force is the centripetal force so
mg-s = mv2/r
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if the speed is greater than or equal to V0 then
- the support force will = 0 and the car will loose contact with the road
- mg =mV0/r
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for a car on a roundabout centripetal force is
the force of friction between the vehicles tyres and the road surface
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so the force of friction is
mv2/r
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for no skidding to occur the force of friction must
- be less than a limiting value F0 and the speed of the vehicle must be less than a certain value V0F0 = mV02/r
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some roads are banked to
enable vehicles to drive round without any sideways friction on the tyres - this enables the speed to be greater .
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for there to be no sideways friction on the tyres due to the road
the horizontal component of the support forces N1 and N2 must act as the centripetal force
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resolving these forces gives
- (N1+N2)sinθ - horizontal
- (N1+N2) cosθ -0 vertical
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if v2 = gr then
theres no sideways friction
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tension at the top is lowest because
- at the top the weight and tension provide the centripetal force mv2/r = mg + R
- at the bottom the weight opposes tension mv2/r = S-mg
- the magnitude of mv2/r is constant round the circle
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on a swing the maximum speed is when
- the spring passes through the lowest position 0.5mv2 = mgΔh
- v2=2gΔh
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at the lowest point S-mg =
mv2/r = m2gh/r
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