Module 5.2 - Circular Motion ✓

Question 1

How do you find the arc length for a section of a circle?

Answer 1

Arc length = angle (rad) * radius

Question 2

How do you calculate angular velocity?

Answer 2

ω = θ/t
ω = 2π/T
ω = 2πf

Question 3

Define angular velocity?

Answer 3

Angular velocity is the rate of change of the angular position of a rotating body

Question 4

How do you calculate linear velocity from an angular velocity?

Answer 4

v = ωr

angle * radius = arc length, as its angular velocity it will be linear velocity

Question 5

Define centripetal acceleration

Answer 5

Centripetal acceleration is the acceleration vector pointed towards the centre of a circle which causes an object to rotate about the centre of that circle

Question 6

Define centripetal force

Answer 6

The force acting on an object moving in circular motion. It acts towards the centre of the circle at right angles to the object’s velocity

Question 7

How do you calculate the work done by a centripetal force?

Answer 7

A centripetal force does no work!

Work done = 0

Question 8

Why do centripetal forces do no work?

Answer 8

Although the centripetal force changes the direction of the object’s motion, it remains perpendicular to the direction of motion of the object. The object does not move towards or away from the centre of the circle so W = Fx = F*0 = 0

Question 9

What are the conditions for simple harmonic motion?

Answer 9

Conditions for SHM:

• An oscillation in which acceleration of an object is directly proportional to the displacement of the object from the midpoint
• This acceleration must be always directed towards the midpoint

Question 10

What are the equations for displacement of an object moving in simple harmonic motion?

Answer 10

If timing began when the object was at a MAXIMUM displacement:
x = Acos(ωt)
If timing began when the object was at a MINIMUM displacement (midpoint):
x = Asin(ωt)

Question 11

What is an isochronous oscillator?

Answer 11

An isochronous oscillator is an oscillator where frequency and period are independent of the amplitude of oscillation
SHM is a form of isochronous oscillation

Question 12

What is the force causing an object to oscillate under simple harmonic motion called?

Answer 12

The restoring force

Question 13

Describe and explain the energy transfers that occur during simple harmonic motion?

Answer 13

At each maximum an object moving under simple harmonic motion only has potential energy. The restoring force does work on the object so transfers some PE to kinetic energy. When the object moves away from the midpoint this energy is transferred back to PE by the restoring force.

Question 14

What is mechanical energy?

Answer 14

Mechanical energy is the sum of the kinetic and potential energies for an object oscillating under simple harmonic motion

Question 15

How do the velocity and acceleration time graphs for an object oscillating under simple harmonic motion relate to its displacement time graph.

Answer 15

• The velocity-time graph is π/2 radians out of phase with the displacement-time graph
• The acceleration-time graph is π radians out of phase with the displacement-time graph (antiphase)

Question 16

What are forced vibrations?

Answer 16

Forced vibrations are vibrations of a system that have been forced to occur by a periodic external force - the driving force

Question 17

Explain the phenomenon of resonance

Answer 17

1) A system can be forced to vibrate by applying a periodic external force at a driving frequency
2) Every system oscillates at its own natural frequency. When the driving frequency approaches the natural frequency the system gains more and more energy as the driving force is applied at regular intervals at the maximum displacements
3) The amplitude of the system rapidly increases as resonance has occurred

Question 18

What are the four different types of damping?

Answer 18

• light damping
• heavy damping
• critical damping
• overdamping

Question 19

What does critical damping do?

Answer 19

Critical damping reduces the amplitude in the shortest possible time

Question 20

How do lightly damped systems react to resonance?

Answer 20

Lightly damped systems have a very sharp resonance peak. Their amplitude will only increase dramatically if the driving frequency is VERY close to the natural frequency

Question 21

How do heavily damped systems react to resonance?

Answer 21

Heavily damped systems have a ‘flatter response’ than lightly damped systems. Their amplitude doesn’t increase nearly as much near the natural frequency and resonate at a broader range of driving frequencies

Question 22

How does increasing the level of damping affect resonance?

Answer 22

Increasing the level of damping makes the amplitude spikes during resonance much less dramatic. It also makes the system resonate to a wider range of driving frequencies.

Also the resonant frequency of the object decreases slightly (although i’m not sure how important this is to know)