Section 6.1 - Further Mechanics

Question 1

What is uniform circular motion?

Answer 1

When an object is rotating at a steady rate

Question 2

What is the speed for a point on the perimeter of a circle?

Answer 2

v = 2πr/T

Question 3

Formula for angular displacement in terms of T?

Answer 3

θ = 2πt/T

Question 4

Formula for angular displacement in terms of f?

Answer 4

θ = 2πft

Question 5

What is angular speed?

Answer 5

The angular displacement per second

Question 6

Formula for angular speed?

Answer 6

ω = 2π/T
or
ω = 2πf

Question 7

What is the unit for ω?

Answer 7

rad/s

Question 8

Formula for velocity in terms of ω

Answer 8

v = ωr

Question 9

What unit is used for measuring angles?

Answer 9

Radians

Question 10

Formula for the arc length?

Answer 10

S= θr

Question 11

Why is an object moving in a circle at constant speed always accelerating?

Answer 11

• Because it has a constantly changing velocity
• Due to the constantly changing direction
• As there is a change in velocity there is a centripetal acceleration

Question 12

What is the formula for centripetal acceleration?

Answer 12

a = v²/r
or
a = rω²

Question 13

Why must there be a centripetal force acting on an object moving in a circle at constant speed?

Answer 13

• Because there is a centripetal acceleration.
• There must be a resultant force acting on the object to makign it accelerate.

Question 14

What direction does the centripetal force act in?

Answer 14

Towards the centre of the circle

Question 15

What is the equation for centripetal force?

Answer 15

F=mv²/r
or
F=mrω²

Question 16

Define amplitude

Answer 16

The maximum displacement from the equilibrium postion

Question 17

What are free vibrations?

Answer 17

Oscillations where the amplitude is constant and are not affected by frictional forces.

Question 18

What is time period?

Answer 18

The time taken for one complete oscillation to occur

Question 19

What is frequncy?

Answer 19

The number of cycles made by an oscillating object

Question 20

What is the formula for angular frequncy?

Answer 20

ω = 2π/T = 2πf

Question 21

Formula for the phase difference bewteen two objects oscillating at the same frequency?

Answer 21

2πΔt/T

Question 22

Definition for SHM

Answer 22

Oscilating motion in which the acceleration is:
* Proportional to the displacement
* Always in the opposite direction to the displacement
* a α -x

Question 23

What is the formula for aceleration?

Answer 23

a = -ω²x

Question 24

What is the formula for displacement?

Answer 24

x = Acos ωt

Question 25

What are the two formula for velocity?

Answer 25

v = -Aωsin ωt
or
v = ± ω √(A²-x² )

Question 26

What is the max velocity?

Answer 26

Vmax = Aω

Question 27

What are the two formula for acceleration?

Answer 27

a = -A ω²cos ωt
or a = -ω²x

Question 28

What is the maximum acceleration?

Answer 28

a max = A ω²

Question 29

Formula for time period of a mass-spring system?

Answer 29

T = 2π √(m/k)

Question 30

Formula for time period of a simple pendulum

Answer 30

T = 2π √(l/g)

Question 31

What does the energy v displacement graph look like?

Answer 31

• Potential energy is a parabolic shape
• Kinetic energy is an inverted parabola
• straighline for total energy

Question 32

When is motion said to be damped?

Answer 32

When dissipasive forces are present

Question 33

What is light damping and give an example?

Answer 33

• The amplitude gradually decreases by a small amount each oscillation
• Displacing a pendulum and letting it come to a stop naturally

Question 34

What is critical damping and give an example?

Answer 34

• reduces the amplitude to zero in the shortest possible time after it has been displaced from equilibrium and released.
• Suspension in a car

Question 35

What is heavy damping and give an example?

Answer 35

• the amplitude reduces slower than with critical damping, but also without any additional oscillations.
• Soft close door

Question 36

What does the displacement time graph look like for each type of damping?

Answer 36

Check notes

Question 37

What is a periodic force?

Answer 37

A force applied at regular intervals

Question 38

What are forced vibrations?

Answer 38

Forced vibrations are where a system experiences an external driving force which causes it to oscillate

Question 39

When does resonance occur?

Answer 39

When the forced vibrations are applied at the natural frequency

Question 40

What is the resonant frequency?

Answer 40

The frequncy at which the maximum amplitude occurs

Question 41

What happens to resosant frequency as the damping that is applied gets stronger?

Answer 41

It gets smaller (shifts to the left)

Question 42

What happens to amplitude as the damping that is applied gets stronger?

Answer 42

It decreases

Question 43

What is the y-int on a resonance graph?

Answer 43

The amplitude of the vibrataion generator

Question 44

2 Applications of resonance?

Answer 44

• Radios - These are tuned so that their electric circuit resonates at the same frequency as the desired broadcast frequency.
• Musical instruments An instrument such as a flute has a long tube in which air resonates, causing a stationary sound wave to be formed.

Question 45

Describe and Explain
Circular motion

Answer 45

• Acceleration is perpendicular to the magnitude of the tangential velocity
• ω = θ/t = 2π/t = 2πf
• v = 2πr/T = ωr
• a = v²/r = rω²
• f = mv²/r = mrω²

Question 46

Describe and Explain
SHM

Answer 46

• Acceleration is proportional to displacement and toward the equilibrium position
• Acceleration velocity and displacement are sinusoidal with respect to time