G484 - Circular Motion and Oscillations

Question 1

Degrees to Radians

Answer 1

x (2π/360)

Question 2

Radians to Degrees

Answer 2

x(360/2π)

Question 3

State, in terms of force, the conditions necessary for an object to move in a circular path at constant speed

Answer 3

Resultant (centripetal force)

Perpendicular to the direction of motion

Question 4

Centripetal Acceleration

Answer 4

Directed towards the centre of the circle
Direction of motion is always changing so velocity is always changing even if speed remains constant
Acceleration is the rate of change of velocity

Question 5

Describe how a mass creates a gravitational field in the space around it

Answer 5

All objects with mass have a gravitational field
The field spreads out into the space around the object in all directions
As a result any other object with mass that is in the field will experience a force of attraction

Question 6

Gravitational Field Strength

Answer 6

Force per unit mass
Close to the earth’s surface, gravitational field strength is approximately equal to the acceleration of free fall
g = -GM/r²

Question 7

Newton’s Law of Gravitation

Answer 7

The force between two point masses is proportional to the product of the masses and inversely proportional to the square of the distance between them

F = - GMm/r²

Question 8

Properties of Gravitational Fields

Answer 8

Unlimited range
Always attractive
Effect all objects with mass
Becomes zero at centre of mass of a sphere as the mass surrounding that point is exerting a force in every direction so the resultant is 0

Question 9

Period

of an object describing a circle

Answer 9

Time taken for the object to complete one circular path

Question 10

Kepler’s Third Law

Answer 10

T² ∝ r³

T² = (4π²/GM)r³

Question 11

Derive T² = (4π²/GM)r³ from first principles

Answer 11

v² = GM/r , v = 2πr/T

(2πr/T)² = GM/r
4π²r²/T² = GM/r
4π²r³ = GMT²
T² = (4π²/GM)r³

Question 12

Geostationary Orbit

Answer 12

24 hour time period
Equatorial orbit - orbits over the equator
Orbits in the same direction as the earth’s rotation
Satellite appears to remain stationary in the sky above a particular point

Question 13

Radian

Answer 13

The angle subtended by an arc of the circumference equal to the radius

Question 14

Displacement

Answer 14

Distance form the equilibrium position

Question 15

Amplitude

Answer 15

Maximum displacement from the equilibrium position

Question 16

Period

Answer 16

Time taken for one complete oscillation

Question 17

Frequency

Answer 17

Number of oscillations completed in one second

Question 18

Angular Frequency

Answer 18

2π x frequency
OR
2π / period

Question 19

Phase Difference

Answer 19

The difference between the pattern of vibration of two points/two waves where one leads or lags begins the other

Question 20

Simple Harmonic Motion

Answer 20

Acceleration is directly proportional to displacement but in the opposite direction i.e. towards the equilibrium position
An object is in S.H.M. if a = -(2πf)² x

Question 21

Simple Harmonic Motion Velocity Equation

Answer 21

v = 2πf √(A²-x²)

Question 22

Simple Harmonic Motion - Period and Amplitude

Answer 22

The period of an object with simple harmonic motion is independent of its amplitude

Question 23

S.H.M. Displacement Graph

Answer 23

Sine curve

Question 24

S.H.M. Velocity Graph

Answer 24

Cosine graph

Question 25

S.H.M. Acceleration Graph

Answer 25

Negative Sine Curve

Question 26

Time Period - Pendulum Equation

Answer 26

T = 2π√(l/g)

Question 27

Time Period - Spring Equation

Answer 27

T = 2π √(m/k) k = spring constant

Question 28

In Phase

Answer 28

Oscillations with the same frequency that reach amplitude at the same time

Question 29

Out of Phase

Answer 29

Oscillations with the same frequency that reach amplitude at different times

Question 30

Damping

Answer 30

Decrease in amplitude of oscillations over time as a result of a resistive force

Question 31

Light Damping

Answer 31

Gradual decrease in amplitude and increase in time period

Question 32

Heavy Damping

Answer 32

Amplitude of oscillation decreases to 0 rapidly and overshoots the equilibrium position before coming to rest

Question 33

Critical Damping

Answer 33

Amplitude decreases to 0 in the shortest possible time

Question 34

Over damping

Answer 34

A very slow return to the equilibrium position

Question 35

Light Damping Example

Answer 35

Sound level meters | Show rapid fluctuations in sound intensity

Question 36

Heavy Damping Example

Answer 36

Car Fuel Gauges So that the pointer does not oscillate Ignores small transient changes in the fuel level in the tank

Question 37

Critical Damping Example

Answer 37

-Pointer instruments e.g. voltmeter, ammeter Pointer reaches correct position after a single oscillation Prevents oscillation around the actual value -car suspension system Passengers don't bounce up and down when the car passes over bumps

Question 38

Natural Frequency

Answer 38

The frequency that an object will vibrate at freely after an initial disturbance

Question 39

Forced Oscillations

Answer 39

When a periodic force is applied to an oscillating object, the object is forced to oscillate at the same frequency as the driver of the periodic force

Question 40

Resonance

Answer 40

Occurs when as oscillating system is forced to vibrate at a frequency close to its natural frequency Amplitude of vibration increases rapidly and becomes maximum when the frequency of the force us equal to the natural frequency

Question 41

Useful Applications of Resonance

Answer 41

``` Driver -> Resonator Cooking - microwaves -> water molecules MRI - radio waves -> nuclei/protons Woodwind Instruments - reed -> air column Brass Instruments - lips -> air column ```

Question 42

Problems Due to Resonance

Answer 42

Driver -> Resonator Engine Vibrations -> Car Windows Wind -> Bridges Earthquake - Ground Vibrating -> Buildings

Question 43

Resonance Without Damping

Answer 43

- amplitude and energy of a resonating system would increase continually - in practise this can never happen as there is always some degree of damping

Question 44

Resonance With Damping

Answer 44

-the amplitude and energy would increase until energy was being dissipated at the same rate as it was being supplied