Circular Motion And Oscillations Flashcards
Define one radian
The angle subtended at the centre of a circle by an arc of length equal to the circles radius
Newton’s law of gravitation
The gravitational force of attraction between two bodies is directly proportional to the product of their masses, and inversely proportional to the square of the distance between them
Define the period T of an object in circular motion
The time taken to complete one revolution.
It is related to the speed v, and the radius r by the equation:
vT = 2 x pi x r
Equation for centripetal force
F = m x v^2
—–
r
What is a field?
The region in which a force operates
What is the gravitational field strength at any point?
The force acting per unit mass at that point
Newtons laws applied to circular motion
F = (m x v^2) / r
Define angular speed
The angle an object rotates through per second
Why are objects travelling in circles accelerating even if they are travelling at constant speed?
Even if the object is going at constant speed, it’s velocity is changing since its direction is changing
Since acceleration is defined as the rate of change of velocity, the object is accelerating even though it isn’t going any faster
Define a period
The period (T) of an object in a circular motion is the time taken to complete one revolution
Speed of an object travelling in a circle?
Distance / time = circumference of circle / period
V = (2 x pi x r) / T
How do you work out centripetal acceleration?
With a constant speed v,
a = v^2 / r
In a direction towards the centre of the circle
Define angular momentum
A property of an object that depends on its angular velocity
Define amplitude, waves (X0)
The maximum displacement of a wave from its mean (or rest) position measured in metres
Define geostationary object
The orbit of an artificial satellite which has a period equal to one day, so that the satellite remains above the same point on the Earth’s equator
From Earth the satellite appears to be stationary
Equations for orbital speed
v = (2 x pi x r) / T
g = v^2 / r
What is an astronomical unit?
The average distance of the Earth from the Sun
Define amplitude, oscillations (X0)
The maximum displacement from the rest or equilibrium position, measured in metres
What is Kepler’s third law of planetary motion?
The square of the period T of a planet is proportional to the cube of its distance r from the Sun
Define gravitational field strength
The GFS at a point is the gravitational force exerted per unit mass on an object at that point
Frequency
The number of oscillations per unit time. unit: Hz
Phase difference
The fraction of an oscillation between the vibration of two oscillating particles
Define amplitude
The maximum displacement of a particle from its equilibrium position
Define angular displacement
The angle through which an object moves in a circle
Define natural frequency
The unforced frequency of a freely oscillating object
Define resonance
The forced motion of an oscillator. Max amplitude is achieved when the forcing frequency matches the oscillators natural frequency
Define simple harmonic motion
Motion of an oscillator where its acceleration is directly proportional to its displacement from equilibrium position and acceleration is directed towards the equilibrium position
Define centripetal force
The net force acting on an object moving in a circle; always directed towards the centre
Define damping
An oscillatory motion where amplitude decreases with time due to energy losses
What is meant by centripetal acceleration?
The acceleration of a body moving in a circle with constant speed acting towards the centre of the circle
What is meant by centripetal force?
The resultant force on an object, acting towards the centre of the circle, causing it to move in a circular path
Define displacement (x)
The distance an object moves from its rest position
May be positive or negative
Define amplitude
The maximum displacement
Always positive
Define frequency
The number of oscillations per unit time at any point
Define period
The mean time for one complete pattern of oscillations to take place at any point
Define phase difference
The angle in radians between two oscillations
Define S.H.M
When the acceleration (a) of an object is proportional to its displacement (x), and the acceleration is in the opposite direction to the displacement
a ∝ -x
The period of an object with simple harmonic motion is ____________ of its amplitude
Independent
For S.H.M. the acceleration of the mass is at a _________ at the midpoint of the oscillations
Minimum
For S.H.M. the acceleration of the mass is ___________ proportional to the displacement
Inversely
