16/17, Circular Motion and Oscillations

Question 1

What is the equation for angular velocity?

Answer 1

ω = θ / t (angular velocity = change in angle / change in time) or ω = 2πf where f is frequency.

Question 2

Equation for tangential velocity?

Answer 2

v = rω (speed = radius * angular velocity).

Question 3

Equation for centripetal acceleration?

Answer 3

a = ω^2 r or a = v^2/r (acceleration = angular velocity squared * radius = speed squared / radius).

Question 4

Equation for centripetal force?

Answer 4

F = ma = mω^2r = mv^2/r (centripetal force = mass * centripetal acceleration).

Question 5

What experiment can find the relationship between radius, force and angular velocity?

Answer 5

Hang a mass through a tube (of a smooth material like glass) and spin an object at the other end, a marker can be used to control the radius and the weight of the mass is equal to the centripetal acceleration.

Question 6

In oscillations what does the term displacement refer to?

Answer 6

The (+/-) distance from the equilibrium position.

Question 7

In oscillations what does the term amplitude refer to?

Answer 7

The maximum displacement.

Question 8

In oscillations what does the term period refer to?

Answer 8

The time taken for one full oscillation.

Question 9

In oscillations what does the term frequency refer to?

Answer 9

The number of oscillations per unit time.

Question 10

What defines simple harmonic motion?

Answer 10

a = -ω^2x (acceleration = -angular frequency squared * displacement, - sign shows acceleration returns the object to the equilibrium position).

Question 11

What experiments can explore SHM?

Answer 11

Can use a spring with a mass on the end, pendulum or glider on air track for example, both can have masses, length of strings and starting amplitude as variables.

Question 12

What shape is a displacement against time graph?

Answer 12

Sine/cosine graph.

Question 13

How can the velocity and acceleration graphs be derived from the displacement graphs?

Answer 13

They are the first and second derivative (also giving a sinusoidal shape).

Question 14

What equations would be used to give the displacement in SHM?

Answer 14

x = A cos ωt (or sine ωt) (displacement = Amplitude * cosine (angular frequency * time).

Question 15

What is the maximum velocity of an oscillator and how is it derived?

Answer 15

From the equation v = +/- ω sqrt(A^2-x^2) it is obvious that a maximum occurs at x = 0 giving maximum velocity = ωA.

Question 16

What types of energy can an oscillator have?

Answer 16

KE, GPE, elastic potential.

Question 17

Characteristics of an oscillator with light damping?

Answer 17

Amplitude decreases slowly over time, frequency is almost unchanged (increases slightly).

Question 18

What is a forced oscillation?

Answer 18

Where a periodic driving force is applied to an oscillator making it oscillate at the driving frequency.

Question 19

What is resonance?

Answer 19

When the driving frequency is equal to the natural frequency of an object.

Question 20

How is pendulums of different heights with one heavier pendulum at a height equal to one of the others all swinging off the same swing an example of resonance?

Answer 20

The pendulum at the same length will have the same natural frequency as the heavier pendulum so the heavier pendulum will drive the lighter one.

Question 21

How quickly would a swinging pendulum with air resistance decay?

Answer 21

Exponentially, you get a sin(x) * e^-x type curve.

Question 22

Examples of resonance being used?

Answer 22

MRI scanners, instruments are often made of a material which resonates with the notes.

Question 23

What happens as you increase damping of a resonating object?

Answer 23

The amplitude at any driving frequency decreases, the maximum amplitude occurs at a lower frequency than the natural frequency and the peak of an amplitude against driving frequency graph gets flatter.