Chapter 6.1: Further Mechanics

Question 1

What kind of force is required to keep an object moving in a circle at a constant speed?

Answer 1

A constant centripetal force. (Applied to the centre of a circle)

Question 2

An object moving in a circle at a constant rate is accelerating. True of false?

Answer 2

True

Question 3

What equation(s) can you use to calculate the magnitude of angular speed (ω)?

Answer 3

ω = v/r or ω = 2πf
ω - s^-1

Question 4

What is angular acceleration in terms of angular velocity?

Answer 4

A = ω^2r

Question 5

What is angular acceleration in terms of velocity?

Answer 5

a = v^2/r

Question 6

What are the equations for centripetal force?

Answer 6

F=mv^2/r or F=mω^2r

Question 7

What is a radian?

Answer 7

The angle of a circle sector such that the radius is equal to the arc length.
Radians are usually written in terms of π.

Question 8

What are the conditions for SHM?

Answer 8

1) acceleration must be proportional to its displacement from the equilibrium point.
2) it must act towards the equilibrium point
3) a is proportional to -x

Question 9

What is the constant of proportionality linking acceleration and x?

Answer 9

-ω^2 or -k/m

Question 10

What is x as a trig function of t and ω?

Answer 10

x=Acos(ωt) or x=Asin(ωt)

Question 11

How can you calculate the maximum speed using ω and A?

Answer 11

Max speed= ωA

Question 12

How can you calculate the maximum acceleration using ω and A?

Answer 12

Max acceleration = ω^2A

Question 13

What is the small angle approximation for sinx?

Answer 13

Sinx = x
Valid in radians

Question 14

What is the small angle approximation for cosx?

Answer 14

Cosx = 1-x^2/2

Question 15

Define free vibrations.

Answer 15

The frequency a system tends to vibrate at in a free vibration is called the natural frequency.

Question 16

Define forced vibrations.

Answer 16

A driving force causes the system to vibrate at a different frequency.

Question 17

Define damping and explain what is critical damping, overdamping and underdamping.

Answer 17

Damping occurs when an opposing force dissipates energy to the surroundings.
Critical damping reduces the amplitude to zero in the quickest time.
Overdamping is when the damping force is too strong and it returns to equilibrium slowly without oscillation.
Underdamping is when the damping force is too weak and it oscillates with exponentially decreasing amplitude.

Question 18

What happens to a vibration with greater damping?

Answer 18

For a vibration with greater damping the amplitude is lower at all frequencies due to greater energy losses from the system. Resonant peak is broader.

Question 19

What are some implications of resonance in real life?

Answer 19

Implications of resonance include that soldiers must break stop when crossing bridges and vehicles must be designed with no unwanted vibrations.