Circular Motion Flashcards
How to calculate the change in angle
Distance moved along circumference / Radius
What is angular velocity
The rate of change of the angle of an object to its centre of rotation as it orbits / rotates
Measured in rads-1
What is the linear velocity of a rotating object
The velocity of the object at a point in time as if it was travelling along a tangent to that point
What is the period of an object in circular motion
The time taken for the object to travel all the way round the circle
What is centripetal acceleration
Rate of change of an object’s velocity
Since the velocity of an object in circular motion is always changing, it is always accelerating.
This acceleration is directed towards the centre of rotation as this is the direction by which the velocity changes
What is centripetal force
The resultant force acting on an object in orbit.
It always acts towards the centre of rotation and is perpendicular to the instantaneous velocity
As the object is accelerating, Fr =ma still appplies, so it is proportional to the centripetal acceleration of the object
What is simple harmonic motion
Oscillating motion in which the acceleration is proportional to displacement and always in the opposite direection to displacement
The object moves one way, then the opposite direction, through its equilibrium position
Describe how simple harmonic motion can be used to explain the motion of a pendulum
As the ball gets further from the centre, its displacement increases, but it decelerates
While as it gets closer back to the centre, its displacement increases, but it accelerates
What is amplitiude
Maximum displacement of an oscillating object from equilibrium
What are free vibrations
Vibrations / oscillations at a systems natural frequency as there is no external force continuosly acting
What are forced vibrations
When an external driving force causes a system to oscillate
What is resonance
What is an objects resonant frequency
Where the amplitude of oscillations of a sytem drastically increase due to gaining an increased amount of energy from the driving force
Occurs most at the resonant frequency, when the driving frequency = Natural frequency
What affect does does damping have on an object in SHM
Decreases the:
Max. Amplitude
Resonant frequency
Sharpness of the peak, so resonance will occur at a wider range of freq.
How may SHM cause a bridge to start violently swinging
People walking across the bridge produce a driving force on the bridge
If the freq, of this force gets too close to the natural frequency, resonance will occur, the bridge will violently swing
What are damped oscillations
When dissipative forces cause energy to dissipate, reducing the amplitude of an object in SHM, due to friction / air resistance
What is light damping
When each cycle takes the same amount of time but the amplitude gradually falls by the same fraction each cycle
What is Critical Damping
Just enough damping to stop the oscillation at equilibrium without it over-shooting , all in the first oscillation after release
What is heavy damping
When the damping is so strong, no oscillating occurs
It slowly returns to equilibrium
How to calculate the Time period of a pendulum in SHM
What are the limitations of this formula
The angle by which the pendulum is displaced must be less than 10 degrees
As in the derivation, you let sin x = x
Describe the energy transfers of a simple pendulum in SHM
Gravitational potential ⇔ Kinetic
How to calculate the time period of a mass - spring system in SHM
What 2 things affect the Frq. / Time period of oscillation of a mass spring system in SHM
Mass
Using Newton’s second law, lower mass decreases acceleration as the resultant force wouldn’t change. So freq. decreases
Strength of spring
Tension - the restoring force - will be less, so by Newton’s second law, acceleration is less
What is the restoring force of an object in SHM
The resultant force that causes the acceleration back to the equilibrium
What are the energy changes in general that take place in SHM
Kinetic Energy ⇔ …Potential Energy
Potential energy is the energy due to the position of the system, is at a maximum when the displacement is at a maximum and a minimum at the equilibrium
Kinetic energy is dependent on speed, which is at a maximum at the equilibrium position and a minimum at the max. amplitude
The total energy stays constant
Describe the relationship between Displacement, Velocity and Acceleration in SHM, in terms of graphs
What do they show
Acceleration is the derivative of Velocity which is the derivative of Displacement
Acceleration is the negative graph of Displacement
