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define angular speed
 the angle turned through per second when an object is in rotation
 unit radians per second

centripetal acceleration
an acceleration towards the center of a circular path

centripetal force
 a force causing an object to move in a circular path ; it acts towards the center
 units Newtons

frequency
 the number of oscillations or waves per second
 units hertz

period
the time taken for one complete oscillation or one full rotation

uniform circular motion
when an object rotates at a steady (constant) rate

angular displacement
 the angle turned through in a given time when an object is in rotation
 units radians

circumference of the wheel

frequency of rotation
f = 1/T where T is the time for one rotation

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

angular displacement (radians) =
 2 pi t / T
 where t = duration and T = time for one rotation
2 pi f

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

angular speed (rad/s) =
2 pi rpm/60

rpm means
revolution per minute

to convert from degrees to radians
/18/pi

to convert from radians to degrees
x 180/pi

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

the velocity of an object in uniform circular motion at any point is
along the tangent to the curve at that point

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

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

for an object whirling round on the end of a spring , the .... is the centripetal force
tension in the string

for a satellite moving round the earth .... is the centripetal force
gravity

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

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

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

the resultant force is
smg

the resultant force is the centripetal force so
mgs = mv^{2}/r

if the speed is greater than or equal to V_{0} then
 the support force will = 0 and the car will loose contact with the road
 mg =mV_{0}/r

for a car on a roundabout centripetal force is
the force of friction between the vehicles tyres and the road surface

so the force of friction is
mv^{2}/r

for no skidding to occur the force of friction must
 be less than a limiting value F_{0} and the speed of the vehicle must be less than a certain value V_{0}
 F_{0} = mV_{0}^{2}/r _{}

some roads are banked to
enable vehicles to drive round without any sideways friction on the tyres  this enables the speed to be greater .

for there to be no sideways friction on the tyres due to the road
the horizontal component of the support forces N_{1} and N_{2} must act as the centripetal force

resolving these forces gives
 (N_{1}+N_{2})sinθ  horizontal
 (N_{1}+N_{2}) cosθ 0 vertical

mv^{2}/r =
(N_{1}+N_{2})sinθ

mg =
(N_{1}+ N_{2}) cos θ


if v^{2} = gr then
theres no sideways friction

tension at the top is lowest because
 at the top the weight and tension provide the centripetal force mv^{2}/r = mg + R
 at the bottom the weight opposes tension mv^{2}/r = Smg
 the magnitude of mv^{2}/r is constant round the circle

on a swing the maximum speed is when
 the spring passes through the lowest position 0.5mv^{2} = mgΔh
 v^{2}=2gΔh

at the lowest point Smg =
mv^{2}/r = m2gh/r

