Further Mechanics

Question 1

If an object is moving in circular motion at a constant speed what two things must there be?

Answer 1

acceleration

centripetal force

Question 2

What 3 equations can be used to calculate the magnitude of angular speed?

Answer 2

ω = 2πf
ω = v/r
ω = Δθ/Δt
where θ is in radians

Question 3

How do you convert degrees to radians?

Answer 3

θ x 2π/360 = angle in radians

Question 4

Define angular velocity.

Answer 4

the rate of change of angular displacement

Question 5

What is angular velocity measured in?

Answer 5

radians per second

Question 6

What is angular displacement?

Answer 6

the angle moved through relative to a specific axis (the angle between the radius of the circle at the initial position and its final position)

Question 7

How is time period, T, calculated?

Answer 7

total time taken / number of rotations

Question 8

What is the velocity, v?

Answer 8

the velocity at which the object is moving around the circle, measured in m/s

Question 9

How is velocity of an object travelling in circular motion calculated?

Answer 9

v = 2πr/T
v = rω

Question 10

Why does an object moving in circular motion have an acceleration even if it is moving with constant velocity?

Answer 10

the angular velocity is always changing as the tangent to the circle at which the body is moving is constantly changing. Even if it is at a constant speed, the direction in which it is moving is changing, meaning its angular velocity is changing. where there is a change in velocity there is acceleration

Question 11

Define acceleration.

Answer 11

rate of change of velocity

Question 12

What is the name given to acceleration due to circular motion?

Answer 12

centripetal acceleration

Question 13

Why does the object have a centripetal force?

Answer 13

F=ma, the body has mass and centripetal acceleration and therefore has a centripetal force holding it in circular motion

Question 14

In which direction does the centripetal force act?

Answer 14

towards the centre of the circle, perpendicular to the velocity.

Question 15

Which factors affect the magnitude of centripetal force?

Answer 15

mass, velocity, radius

Question 16

Which equations can be used to calculate centripetal acceleration?

Answer 16

a = v^2 / r
a = ω^2 x r

Question 17

Which equations can be used to calculate centripetal force?

Answer 17

F = mv^2 / r
F = m x ω^2 x r

Question 18

Which equation can be used to calculate the force on an object?

Answer 18

F - Fr = ma

Question 19

What is an example of a centripetal force?

Answer 19

friction
gravity
tension

Question 20

What is represented by μ in the equation Fr = R x μ

where Fr is the frictional force and R is the resultant force (often equal to mg)

Answer 20

the coefficient of friction between the object and the surface

Question 21

How do you calculate the greatest speed a car can do without losing contact with the ground?

Answer 21

Friction = mv^2 / r
Friction = μmg

so max v = the square root of μmg

Question 22

What condition is necessary for simple harmonic motion to occur?

Answer 22

a ∝ -x

where a is the acceleration and x is the displacement

Question 23

What equation can be used to calculate the acceleration of an object inn simple harmonic motion?

Answer 23

a = ω^2 x (x)

Question 24

What is an oscillation defined as?

Answer 24

a simple repeated motion. when a system moves between 2 points through a mean position over the same period of time

Question 25

What are two common examples of systems which display simple harmonic motion

Answer 25

a pendulum on a string | a mass spring system

Question 26

How does energy change as a spring moves through a complete oscillation?

Answer 26

``` At top : Ep In middle : max Ek At bottom: min Ek In middle: max Ek At top: Ep ```

Question 27

Which equation can be used to calculate the time period, T of a mass spring system?

Answer 27

T = 2π x square root of m/k | where k is the spring constant

Question 28

Which equation can be used to calculate the time period, T of a simple pendulum system?

Answer 28

T = 2π x square root of l/g | where l is the length og the pendulum and g is the acceleration due to gravity

Question 29

What equation gives the displacement of an object at any given time during simple harmonic motion?

Answer 29

x = Acos(ωt)

Question 30

How do you calculate the equation for velocity from the equation for displacement? (or acceleration from velocity)

Answer 30

integrate the equation (the area under the curve) (x = Acos(ωt) becomes v = -ωAcos(ωt)) where A is amplitude

Question 31

When a free vibration is allowed to oscillate it does so with what?

Answer 31

Natural frequency, f zero | everything has an f0

Question 32

What is resonance?

Answer 32

When the driving force oscillates at the same frequency as the object, they interfere and the amplitude becomes very large.

Question 33

How does damping impact the amplitude of an object in resonance?

Answer 33

Large damping = lower amplitude Light damping = medium amplitude No damping = large amplitude

Question 34

On a graph of amplitude against driving frequency, the amplitude is greatest at which point?

Answer 34

f zero (natural frequency)

Question 35

Which equation can be used to calculate the velocity of an object at any given moment in simple harmonic motion?

Answer 35

v = +or- ω x square root of A^2 - x^2