Further Mechanics

Question 1

What is angular speed?

Answer 1

The angle an object rotates through per second. ω = θ / t

Question 2

What is frequency in circular motion?

Answer 2

Number of complete revolutions per second. f = 1 / T

Question 3

What is time period in circular motion?

Answer 3

The time taken for one complete revolution. T = 1 / f

Question 4

Where does the velocity of an object in circular motion act?

Answer 4

At a tangent to the circle.

Question 5

Where does the centripetal acceleration of an object in circular motion act towards? How can it be calculated?

Answer 5

It’s directed to the center of the circle (always perpendicular to the velocity)
a = v² / r = ω²r

Question 6

In what direction does the centripetal force act and how can it be calculated?

Answer 6

The centripetal force acts towards the center of the circle. F = ma = mv² / r = mω²r

Question 7

What equation links an object in circular motion on a slop of angle θ, velocity v and a radius r?

Answer 7

tanθ = v² / gr

Question 8

What are the conditions for simple harmonic motion?

Answer 8

Displacement and acceleration are in opposite directions (a = -ω²x)
Displacement and acceleration are directly proportional to each other

Question 9

How are frequency and time period defined in SHM?

Answer 9

Time period is the time taken for one cycle (a how long it takes for the object to get back to it’s starting position)
Frequency is the number of cycles per second

Question 10

What do the frequency and time period of an oscillation not depend on in SHM?

Answer 10

The amplitude of the oscillation

Question 11

Where does an object’s maximum acceleration occur at in SHM?

Answer 11

At the maximum magnitude of it’s displacement (where the displacement = amplitude)
a_max = ± ω²A

Question 12

What are the energy changes in SHM?

Answer 12

An object in SHM exchanges kinetic and potential energy as it oscillates.
For a spring it will be elastic potential energy and for a pendulum it will be gravitational potential energy.

Question 13

Where is kinetic energy at a maximum in SHM?

Answer 13

At equilibrium position
Equilibrium position is where velocity is at its maximum
E_k = 1/2 mv²

Question 14

Where is potential energy at its maximum in SHM?

Answer 14

At the maximum displacement (or where displacement = amplitude)

Question 15

What is mechanical energy in SHM?

Answer 15

The sum of the potential and kinetic energy
It stays constant providing the motion isn’t damped

Question 16

What are free vibrations?

Answer 16

They involve no transfer of energy to or from the surroundings
They have constant amplitude
They occur at the resonant/ natural frequency of the system

Question 17

What are forced vibrations?

Answer 17

They happen when there is a periodic external driving force
This force has a frequency called the driving frequency (the frequency the system is forced to oscillate at)

Question 18

What is resonance?

Answer 18

A phenomenon that can occur during forced vibrations
When the driving frequency approaches the resonant/ natural frequency, energy is gained from the driving force, amplitude increases
When the driving frequency = resonant frequency, resonance occurs and the maximum amplitude is reached

Question 19

At resonance what is the the phase difference between the oscillator and the driver?

Answer 19

90 degrees (or π/2 radians) out of phase

Question 20

When the driving frequency is lower than the natural frequency, what is the phase difference between the driver and the oscillator?

Answer 20

They are in phase

Question 21

When the driving frequency is greater than the natural frequency, what is the phase difference between the driver and the oscillator?

Answer 21

They are in anti-phase (or 180 degrees or πradians out of phase)

Question 22

What is damping?

Answer 22

When an oscillating systen loses energy to its surroundings due to frictional forces (called damping forces)
Systems can be damped to stop oscillations or minimise the effect of resonance

Question 23

What does damping do?

Answer 23

It reduces the amplitude of the oscillation over time
This is because energy is directly proportional to the amplitude squared
v_max = ωA, E_k = 1/2 m(ωA)²

Question 24

What is a lightly damped system?

Answer 24

These systems take a long time to stop oscillating
Their amplitude only reduces by a small amount each period
They have a sharp resonance peak (amplitude only increases dramatically when the driving force is very close to the natural frequency)

Question 25

What is a heavily damped system?

Answer 25

These systems take less time to stop oscillating
Their amplitudes become much smaller each period
They have a broader resonance peak (they have less sensitivity to the driving, frequency)
Their resonanct frequency becomes slightly lower

Question 26

What is critical damping?

Answer 26

It reduces the amplitude (stops the system from oscillating) in the shortest possible time

Question 27

What is overdamping?

Answer 27

When the oscillations are stopped but it takes the system longer to return to equilibrium than a critical damped system.