Periodic and Circular Motion

Question 1

What is Linear Velocity?

Answer 1

The rate of change of linear displacement

Question 2

What is Angular Velocity?

Answer 2

The rate at which an object rotates relative to its axis of rotation.

Question 3

What is the SI unit of angle?

Answer 3

Radians

Question 4

What are the units and symbol of Angular Velocity?

Answer 4

Units: Rads^-1
Symbol: ω

Question 5

How many radians are in a complete circle?

Answer 5

2π

Question 6

What is the equation of Linear Velocity?

Answer 6

v = 2πr/T = 2πrf

Question 7

What is the equation of Angular Velocity?

Answer 7

ω = 2π/T = 2πf = v/r

Question 8

Whaich direction is acceleration in circular-motion?

Answer 8

Towards the axis of rotation

Question 9

What is the equation for Centripetal Acceleration?

Answer 9

a = v²/r = ω²r

Question 10

What is the equation for Centripetal Force?

Answer 10

F = mv²/r = mω²r

Question 11

What direction is Centripetal Force acting in?

Answer 11

Towards the axis of rotation

Question 12

Define Simple Harmonic Motion (SHM)?

Answer 12

It is a special type of circular-motion.

The acceleration is proportional to displacement and acts in the opposite direction.

Question 13

Where is Dislpacement at its Maximum and Minimum?

Answer 13

Maximum: At Amplitude
Minimum: At Equilibrium

Question 14

Where is Velocity at its Maximum and Minimum?

Answer 14

Maximum: At Equilibrium
Minimum: At Amplitude

Question 15

Where is Accerleration at Maximum and Minimum?

Answer 15

Maximum: At Amplitude
Minimum: At Equilibrium

Question 16

What is the equation for calculating the displacement at any time?

Answer 16

x = A Cos(ωt) = A Cos(2πft)

Question 17

What are the units and symbol for Displacement?

Answer 17

Units: Meters (m)
Symbol: X

Question 18

What are the units and symbol for Amplitude?

Answer 18

Units: Meters (m)
Symbol: A

Question 19

What is the equation for acceleration at any time?

Answer 19

a = -ω²X = -(2πf)²X

Question 20

What is the equation Maximum Acceleration?

Answer 20

a = ± ω²A = ±(2πf)²A

It is ± as it occurs on both side of equilibrium.

Question 21

What is the equation for Velocity at any time?

Answer 21

v = ±ω(A²-X²)^0.5 = ±2π(A²-X²)^0.5

Question 22

What is the equation for maximum Velocity?

Answer 22

v = ±ωA = ±2πfA

Question 23

What is the equation for Total Energy of an SHM oscillator?

Answer 23

E=0.5mω²A²

Question 24

What are two SHM oscillators?

Answer 24

Mass-Spring System

Simple Pendulum

Question 25

What is the equation for the Period of a Mass-Spring System?

Answer 25

T = 2π(m/k)^0.5

Question 26

What does the equation for the Period of a Mass-Spring System assume?

Answer 26

The spring obeys Hookes Law | The spring is not stretched beyond its elastic limit

Question 27

What is the equation for the Period of a Simple Pendulum?

Answer 27

T = 2π(l/g)^0.5

Question 28

What does the equation for the Period of a Mass-Spring System assume?

Answer 28

The pendulum is only displaced by a small angle

Question 29

What is the equation for the Maximum Kinetic Energy of a SHM oscillator?

Answer 29

E = 0.5mω²A²

Question 30

What is the equation for the Kinetic Energy at any point in an SHM oscillator?

Answer 30

E = 0.5mω²(A²-X²)

Question 31

Where is Kinetic Energy at its Maximum and Minimum in and SHM oscillator?

Answer 31

Maximum: At Equilibrium Minimum: At Amplitude

Question 32

Where is Potential Energy at its Maximum and Minimum in and SHM oscillator?

Answer 32

Maximum: At Amplitude Minimum: At Equilibrium

Question 33

Where does Kinetic Energy and Potential Energy intercect on a Displacement-Energy graph?

Answer 33

At 0.5 E | As half the energy is kinetic and half is potential

Question 34

What is a Damped Oscillator?

Answer 34

An Oscillator which loses energy to their surroundings.

Question 35

What doesn't change when an oscillator is damped?

Answer 35

The Period remains the same

Question 36

what is thetotal energy of an oscillator proportional to?

Answer 36

The square of its displaement | X²

Question 37

What is the defintion of an SHM oscillator?

Answer 37

a ∝ -x

Question 38

What is meant by Free Oscillator?

Answer 38

An Oscillator with no damping

Question 39

What is meant by Light Damping?

Answer 39

A system with (exponentially) decreasing amplitude

Question 40

What is meant by Heavy damping

Answer 40

A system that takes a long time to reach the equilibrium position

Question 41

What is meant by Critical Damping?

Answer 41

A system that reaches equilibrium and comes to rest in the shortest possible time ≈ t/2

Question 42

What is an example of Light Damping?

Answer 42

Mass-Spring or Pendulum

Question 43

Does the period change when an oscillator id lightly damped?

Answer 43

No | The period doesn't change

Question 44

What is an example of Heavy Damping?

Answer 44

Mass-Spring in a high viscosity fluid

Question 45

Wha is an example of Critical Damping?

Answer 45

Car Suspension

Question 46

Who desires Critical Damping and why?

Answer 46

Engineers | It limits vibration, as it returns to equilibrium then stops

Question 47

Define Natural Frequency?

Answer 47

The frequency at which a system resonates when not subjected to an external force

Question 48

What is the equation for the Natural frequency of a Mass-Spring System?

Answer 48

f=(1/2π)(k/m)^0.5

Question 49

What is the equation for the Natural frequency of a Pendulum?

Answer 49

f=(1/2π)(g/l)^0.5