Further Mechanics Flashcards
Angular Speed
The angle an object rotates through per second
symbol = w
measured in
Equation for angular speed
w = theta / t
theta = angle that the object turns through in rad
w = v/r
v = linear speed
r = radius
Centripetal acceleration
Objects travelling in circles are accelerating since their velocity are changing
even if a car is going at constant speed, their velocity would change as their direction is changing
since acceleration is the rate of change of velocity, the object is accelerating even though its not going any faster
centripetal acceleration is always directed towards the centre of the circle
a ball moving at a constant speed in a circle
because the ball is always chaging direction, the linear velocity is always changing
however the the magnitude of the of the linear velocity is always the same
equations for centripetal acceleration
a = v v / r
v = magnitude of linear velocity
a = w w x r
w = angular speed in ras s ^-1
centripetal force
Using newtons first law we know that since objects travelling in a circle has centipetal acceleration, there must be a force casuing this acceleration
This force is called centripetal force and acts towards the centre of the circle
Remove this force then the object will fly off at a tangent with velocity, v
centripetal force equations
F = MV^2 / r
F = m w^2 r
What is simple harmonic motion
An object moving with SHM oscillates to and from, either side of an equilibrium position
This equilibrium is the midpoint of the objects motion
distance of the object from the equilibrium is called its displacement
restoring force
There is always a restoring force pulling or pushing the object back towards the equilibrium position
Size of this force depends on the displacement
The restoring force makes the object accelrate towards the equilibrium
Simple Harmonic Motion can be defined as
An oscillation in which the accelertaion of an object is directly proportional to its displacement from its equilibrium position and is directed towards the equilibrium
a = -x
a = accelartion
x = displacement
SHM
displacement
Displacement, x, varies as a cosie or sine wave with a maximum value, A (the amplitude)
SHM
velocity
Velocity, v is the gradient of the displacement-time graph
it has a max vlaue of wA (where w is the angular frequency of the oscillation )
w = 2pi f
SHM
Acceleration
the gradient of the velocity-time graph
it has a max value of w^2 A
SHM graphs
when gradient of displacent time graph is 0, velocity is zero
When gradient of velocity time graph is at max, acceleration is at max
phase difference
a measure of how much one wave lags behind another
two waves in have have a PD of 0 or 2pi radians
SHM
Potencial and kinetic energy
an object in SHM exchanges potencial energy and kinetic energy as it oscillates
type of potencial energy depends on what is providing the restoring force
This will be gravitational Ep for pendulums and elastic Ep ( elastic strain energy) and possibly gravitational Ep for masses on strings
potential and kinetic energy evaluation
-As the object moves towards the equilibrium position, the restoring force does work on the object and so transfers some Ep to Ek
-When the object is moving away from the equilibrium, all that Ek is transferred back to Ep
-At the equilibrium, the objects Ep is said to be zero and its Ek is maximum, therefore its velocity is maximum
-At the max amplitude on both sides of the equilibrium, the objects Ep is maximum and its Ek is zero - so its velocity is zero
mechanical energy
sum of kinetic and potential energy
stays constant as long as the motion isn’t damped
The energy transfer for one complete cycle of oscillation is: Ep to Ek to Ep etc.
a mass on a spring
a mass on a spring is a simple harmonic oscillator (SHO)
when the mass is pushed or pulled either side of the equilibrium position, theres a restoring force exerting on it
