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Module 5 - Chapter 16 - Circular motion - Coggle Diagram
Module 5 - Chapter 16 - Circular motion
Radian
Angle subtended by a circular arc with a length equal to the radius of a circle
Angle in radian =
360 degrees =
To convert from degrees to radians divide by
Angular velocity
Angular velocity is the rate of change of angle
In a time equal to one period, the object moves through an angle of
,
Angular velocity is measured in raidans per second
centripetal acceleration
centripetal force
Any force that keeps a body moving with a uniform speed along a circular path
always perpendicular to the velocity of the object
Force has no component in the direction of motion so no work is done on it, and speed is constant
Objects travelling in a circle have a direction that's constantly changing, and velocity is also constantly changing
Angular and linear velocity
(distance/time)
since
,
For objects with same angular velocity, linear velocity is directly proportional to the radius
Centripetal acceleration
Acceleration of any object travelling in a circular path at constant speed (alwys acts towards the centre)
from
, we get
centripetal force
Combine F = ma and a = v^2/r
For constant mass and radius, centripetal force is directly proportional to the veloctiy squared
Since v = wr, we can say that
Force is always towards towards the centre of the circular path
Investigating circular motion
Tie a bung with mass m to a piece of string and thread it through a glass tube
Other end of string has weight with mass M suspended from it, this provides centripetal force F=mg as tension is constant
String is whirled and time taken for one rotation is measured
Alter the mass and repeat
Plot a graph of v^2 against M, and a straight line passing through origin should be produced
Source of centripetal force
Banked surface
Greater speed required greater centripetal force
Velodrome tracks are banked, as a horizontal component of normal contact force and firction from tyres provide force required to follow the path
Fair ground
When an object that moves in a ferris wheel is stationary, the normal contact force equals the person's weight
When the wheel rotates, net force is required to travel in a circular path
At top, F = mg-N so N reduces and you feel lighter
At bottom, N increases providin a net force upwards towards the centre
Can come from many places, when an object experiences multiple forces, the resultant force must be used
Conical pendulum
Pendulum rotates at constant speed
Horizontal component of force provides centripetal force required for the circular motion of the pendulum
Vertical component equals the weight of the pendulum (no acceleration in vertical direction)
Angle of pendulum isn't affected by mass
