Mechanics/ biomechanics - unit 1 deck 1

Question 1

Describe what is meant by saying ‘the choice of scale for a unit’

Answer 1

This is referring to the size range of any particular type of unit.

e.g. the main metric unit of distance is the metre but you have a choice of also using micrometres, millimetres, centimetres or kilometres. These different choices is a choice of scale

Question 2

What is the single system of units referred to as ?

Answer 2

System Internationale d’Unites - known as SI units

This is just a system which came up with the standard units you should use

Question 3

What are the 3 main base units in Systeme Internationale (SI) relevant to this module ?

Answer 3

1. The metre (m) - the standard unit of length
2. The second (s) - the standard unit of time
3. The kilogram (kg) - the standard unit of mass

Question 4

What is the 4th base SI unit which we should know about relevant to the biomechanics module?

Answer 4

kelvin (K) - the standard SI unit of temperature.

Question 5

What is the relevant supplementary unit in the SI system which is relevant to this module ?

Answer 5

The radian (rad) - the standard unit of angle

Question 6

What are the units other than the base SI units and supplementary SI units referred to as and how are they formed ?

Answer 6

The are referred to as derived units and are formed by combining base units

e.g. the newton (N) is equivalent to kilogram metres per second squared (kg m s^-2 )

Question 7

What do each of the following scale factors that you should remember stand for:

• mega (M) -
• kilo (K) -
• centi (c) -
• milli (m) -
• micro (µ) -

Answer 7

1. mega (M) - x10⁶
2. kilo (K) - x10³
3. centi (c) - x10^-2
4. milli (m) - x10^-3
5. micro (µ) - x10^-6

Question 8

What are the 3 rules you need to remember to follow when using units ? i.e. m, cm, km, s, etc etc

Answer 8

1. Write prefixes without a space, e.g. cm (there is no space between the c and the m)
2. Leave a space between symbols for units e.g. m s^-1 (metres per second) not ms^-1 as this reads as ‘‘per millisecond’’
3. Never pluralise units, e.g. 10ms means 10 milliseconds not 10 metres

Question 9

What are the 4 basic physical quantities and state their SI units that we should know about in mechanics and biomechanics

Answer 9

1. Time - SI unit is seconds (s)
2. Distance - SI unit is meters (m)
3. Angle - SI unit is radian (rad), note that the common unit of angle is the degree
4. Temperature - SI unit is kelvin (K)

Question 10

What are the common units of temperature used ?

Answer 10

Degrees Celsius, represented by the symbol °C

Question 11

What is the Celsius scale based on ?

Answer 11

The melting and bioling point of water

• 0 degrees = melting point of water
• 100 degrees = bioling point of water

Question 12

What does 0K represent and what is this the equivalent of in degrees Celsius ?

Answer 12

0K = abolsute zero, the point at which matter has no energy, this is equal to -273 degrees Celsius

Question 13

Define the radian (rad)

Answer 13

One radian is encloses an arc which has a length equal to the circle radius

Question 14

What is the relationship of radians to a full revolution (360 degrees)?

Answer 14

2π radians = a full revolution (360 degrees)

Note for maths purposes ignore the names and have it as 2π = 360

Question 15

What does pi represent ?

Answer 15

It represents a constant, the ratio of the circumference of a circle to its diameter, it is the same for all circles

Question 16

What is the equation for converting between radians and degrees ?

Answer 16

The more formal equation is in page 4 of mechanics binder

Question 17

What is the difference between scalar and vector quantities

Answer 17

A scalar is a quantity that has a magnitude only

A vector is a quantity that has a magnitude and direction

Question 18

Describe the difference between distance and displacement

Answer 18

• Distance is simply the total distance travelled regardless of direction; it is a scalar quantity
• Displacement is a straight-line distance and a defined direction; it is a vector quantity

Question 19

Describe the difference between angular distance and angular displacement

Answer 19

• An angular distance is simply the total angle turned through
• Whereas angular displacement has a magnitude (the angle it is turned through) and direction (the direction of the rotation about an axis); it is a vector quantity e.g. consider a bath tap if you instructed someone to turn a bath tap you would tell them both the direction and the angle through which to turn it

Question 20

How are scalar quantities added together ?

Answer 20

They can be added using simple rules of arithmetic, there is nothing new to learn for this

e.g. 1kg + 2kg = 3kg

Question 21

What are the two main methods for adding or subtracting vectors together ?

Answer 21

1. Combining vectors graphically
2. Resolving using trigonometry

Question 22

What is the term used to describe the vector produced when two or more vectors are added or subtracted ?

Answer 22

The resultant vector

Question 23

Describe the basic idea behind using trigonometry for resolving vectors

Answer 23

• The basic idea is to replace each vector with a pair of vectors ar right-angles to each other.
• This is called resolving the vector into its components, the resolved vectors along each direction can then be added to give the components of the resultant vector

Question 24

Why do you often work in degrees when using trigonometry when the SI unit for angles is radians ?

Answer 24

Because it is easier to visualise degrees and calculators are naturally set to work in degrees not radians

Question 25

Which is the preferred method for combining vectors ?

Answer 25

Using trigonometry

Question 26

Look over pages 8&9 in binder to see the worked examples of resolving vectors using trigonometry

Question 27

What are all positions and directions in mechanics and biomechanics given in relation to ?

Answer 27

A reference frame

The choice and position of the reference frame will be dependent upon the movement being studied. For example, if you are interested in the movement of someone walking then you will probably use a reference frame fixed on the ground. However, if you were interested in how the head moves during walking then you may choose the reference frame to be fixed on the trunk.

Question 28

When the position and motion of objects are stated, it is important that they are given in relation to some kind of reference frame, the positions within a reference frame need to be related, this is done with a co-ordinate system, what are the 2 main co-ordinate systems we should know about ?

Answer 28

1. The rectangular co-ordinate system
2. The polar co-ordinate system

Question 29

Describe the basic three-dimensional rectangular co-ordinate system

Answer 29

This is the Caresian system - it consists of three axis at right angles to each other, normally labelled as x, y & z axis. A simple way to imagine this is as three edges of a cube.

For a three-dimensional system, three co-ordinates (x, y, z) give the position of a point. The co-ordinates of the origin (the point where all axes cross) are (0, 0, 0)

Question 30

What are the axes in a rectangular co-ordinate system when considering 2 dimensions?

Answer 30

The x and y axes

Question 31

Go over the worked example on Pg. 11 in the binder for Cartesian systems

Question 32

When axes are all at right angles to each-other, as in the cartesian system what are they said to be ?

Answer 32

They are said to be orthogonal

Question 33

What is special about orthogonal axes ?

Answer 33

They are independent of each other; a change in position on one axis does not result in a change in position on another one

e.g. imagine yourself travelling along the x-axis, your position on that axis will change but your position on the y & z axes will remain the same.

Question 34

Describe what a plane is in maths

Answer 34

A plane is a flat surface (like a thin sheet of paper) it is regarded as having zero thickness and is therefore two-dimensional

Pic below shows 3 different planes

Question 35

Here are some facts about planes that are important to remember:

1. Two planes can be at right-angles to each other
2. Three planes but no more, can mutually be at right angles, as at the corner of a cube
3. A straight line is formed where two planes cross each other

Question 36

Are angles given in the cartesian co-ordinate system ?

Answer 36

No - this doesn’t mean it couldn’t be calculated however

Question 37

What is the main difference between polar co-ordinates and rectangular co-ordinates ?

Answer 37

In polar co-ordinates angles are also used to describe positions

Question 38

Describe what is meant by polar co-ordinates

Answer 38

In 2-D this means giving the angle of the line and its length (r_c, θ_c) Look at the worked example on Pg 14

In 3-D this means giving a distance and 2 angles (r, θ, ϕ) look at the example on Pg 15

Question 39

When are polar co-ordinates more useful than rectangular co-ordinates ?

Answer 39

In studies of circular objects and when angles and rotations are important.

In biomechanics, polar co-ordinates can be useful in describing the motion of joints. For example, in the sagittal plane (two dimensions only) the position of the knee joint can be described relative to the trunk using an angle and a length. In this case, the angle describes the flexion and extension of the hip joint and the length describes the length of the thigh.

Question 40

What term is used to describe the movement of an object in a circular path around an axis with no translation taking place ?

Answer 40

A rotation

Question 41

What is kinematics ?

Answer 41

This is the study of motion (or movement), it is concerned with the ways in which objects move but not with the causes of movement (the causes of movement are forces)

Question 42

What is the two distinct ways in which movement can occur ?

Answer 42

1. A linear (or translational) motion
2. A rotary (or rotational) motion

Question 43

An object can only undergo linear or rotatory motion but not at the same time - T or F?

Answer 43

False - An object may undergo either linear or rotary motion or both at the same time.

e.g. a car travelling along a straight road is undergoing linear motion, a windmill rotating about its central axis is undergoing rotary motion, and a football rolling along the ground moves in a straight line and rotates as well - it is undergoing both linear and rotary motion at the same time.

Question 44

What type of movement can joints undergo

Answer 44

Joints may only undergo rotary motion, rotating about the joint centre, yet by working together the joints can result in an overall linear motion.

e.g. during walking the combined rotations of the joints of the lower limbs result in overall linear motion

Question 45

Describe what is meant by the term movement constraints

Answer 45

This is when an object has limited movements

• e.g. you could have a cup in your hand which you can move up and down, forward and back, and from side to side. You can also rotate the cup in any way thus the cup is free to move in all possible ways.
• On the other hand you could have a door which is only free to rotate about an axis through its hinges, this is termed constrainted movement

Question 46

What term is used to describe the movement of an object in a straight line with no rotation ?

Answer 46

A translation

(think of this with reference to a cartesian system)