Circular and Simple Harmonic motion Flashcards
What is the definition of an angle in radians?
It is defined as the arc-length divided by the radius of the circle
What is angular speed?
It is defined as the angle turned per unit time
What is an angle in radians?
It is defined as the arc length divided by the radius of the circle
What is the frequency?
The number of complete revolutions per second
What is the time period?
The time taken for a complete revolution
What is acceleration?
It is the rate of change of velocity
What is the centripetal acceleration?
The acceleration of an object in circular motion is towards the centre of the circle
What is the centripetal force?
If there is a centripetal acceleration, then there must be a force acting towards the centre of the circle
How do you calculate the tension in vertical circles from the top of the circle?
T= mv^2/r - mg
How do you calculate the tension in vertical circles from the bottom of the circle?
T=mv^2/r + mg
How would you calculate the centripetal force on a car driving over a hill?
mg-R = mv^2/r
How would you calculate the speed of a vehicle on a banked track?
v^2 = grtan(angle of the bank)
What is simple harmonic motion?
It is defined as oscilating motion in which the acceleration is proportional to the displacement and always in the opposite direction to the displacement
What are the conditions for SHM?
The acceleration is directly proportional to the displacement
The acceleration is always in the opposite direction to the displacement
What is responisible for an object in SHM moving back towards the equilibrium position?
The restoring force
What is the relationship between the size of the restoring force and the displacement?
The size of the restoring force is directly proportional to the displacement
When is the velocity of an object in SHM maximum?
At the equilibrium position, when the acceleration = 0.
When is the acceleration of an object in SHM maximum,
At the maximum displacement(+/-), when velocity = 0.
Describe the motion of an object moving in SHM, in terms of kinetic and potential energy as it moves through the equilibrium position.
As the object moves toward the equilibrium, the restoring forces do work on the object and transfer some potential energy to kinetic energy.
As the object moves away from the equilibrium, all the kinetic energy is transferred to potential energy.
At equilibrium, the potential energy is zero and kinetic energy is maximum.
Describe the motion of an object in SHM, in terms of kinetic and potential energy at maximum displacement.
At maximum displacement(+/-), the kinetic energy is zero and the potential energy is maximum.
What is mechanical energy?
It is the sum of the kinetic and potential energy and it is constant ass long as the motion isn’t damped.
Describe the displacement-time graph for an oscillating object
It varies as a cosine with a max value of A(amplitude)
Describe the velocity-time graph for an oscillating object
It is the gradient of the displacement-time graph. It has a max value of ωA(ω-angular frequency of the oscillation) and is a quarter of a cycle in front of the displacement.
Describe the acceleration-time graph for an oscillating object
It is the gradient of the velocity-time graph. It has a max value of ω^2A and is in antiphase with the displacement
Give examples of simple harmonic oscillators
A mass on a spring
A simple pendulum
Which factors affect the time period of a mass on a spring?
The spring constant
The mass on the spring
Which factor doesn’t affect the time period of a mass on a spring?
The amplitude
Which factor affects the time period of a simple pendulum?
The length of the rod/string of the pendulum
Which factors don’t affect the time period of a simple pendulum?
The mass of the pendulum
The amplitude
What happens in free vibrations?
There is no energy transfer to and from the surroundings and the vibrations oscillate at a natural frequency
When do forced vibrations occur?
Forced vibrations occur when there is an external driving force
What happens when the driving frequency is less than the resonant frequency?
Then they are in phase and the oscillator follows the motion of the driver
What happens when the driving frequency is greater than the resonant frequency?
They are out of phase and at resonance. the phase difference between the driver and oscillator is 90.
When does resonance occur?
It occurs when the driving frequency is equal to the reonant frequency
What happens when the driving frequency approaches the resonant frequency?
The system gains more and more energy from the driving force and vibrates with a rapidly increasing amplitude. When this happens, the system is resonating.
Give examples of resonance
- Organ pipe- the column of air resonates which sets up a stationary wave
- A swing-a swing resonates when someone pushes the swing at its resonant frequency
What is damping?
Damping is when an oscillating system loses energy to its surroundings due to frictional forces
What are the different types of damping on a system?
Undamped
Lightly-damped
Critically damped
Overdamped
What happens in an undamped system?
The amplitude is constant
There is no energy transfer out of the system
What happens in a lightly damped system?
The amplitude of the oscillation decreases slowly but oscillation continues
What happens in a critically damped system?
The amplitude of the oscillation gets reduced in the shortest possible time
What happens in an overdamped system?
The system takes longer to return to equilibrium than a critically damped system. There is no oscillating motion.
How does damping affect resonance?
Lightly damped systems have a very sharp resonance peak.
Heavily damped systems have a flatter response.
How is critically damping used in everyday life?
Car suspension systems and moving coil meters are critically damped so they don’t oscillate.
