Mechanics unit 2 (this is a continuation of mechanics and biomech unit 1) - deck 6

Question 1

State the equation used for calculating tangential linear velocity

Answer 1

v = r ω

v = the tangential linear velocity which is the linear magnitude of the angular velocity and is directed at a tangent to the circle formed by the motion (essentially is the linear velocity at a specific point) e.g.a ball is rotating around a point attached at the end of a string and then is cut, v would be the linear velocity the ball would have as the string is cut

r = the radius

ω = angular velocity

Question 2

When considering the acceleration of something undergoing angular motion what are the 2 components of acceleration to consider?

Answer 2

1. The 1st is the component which acts to change the magnitude of the velocity (tangential acceleration)
2. The 2nd is the component which acts to change the direction of the body (radial acceleration)

Question 3

Define what the tangential acceleration of a body undergoing angular motion is

Answer 3

It is the linear acceleration directed at a tangent to the circle formed by the angular motion.

Question 4

When is the tangential acceleration equal to zero ?

Answer 4

During uniform angular motion (i.e. when the body rotates with a constant angular velocity)

Question 5

State the equation used to calculate tangential acceleration

Answer 5

a_t = r α

• a_t = the tangential acceleration
• r = radius
• α = angular acceleration

Question 6

Define what the centripetal/ radial acceleration is of a body undergoing angular motion

Answer 6

This is the acceleration which acts to maintain the body on its circular path. It is directed from the body to its centre of rotation

e.g. consider a ball rotating on the end of a piece of string, the acceleration acts along the string and the force is equivalent to the tension in the string (think of this as frictional force in the worked example later on)

Question 7

What is the meaning of centripetal ?

Answer 7

This means towards the centre

Question 8

Why does there need to be a radial acceleration for a body to have angular motion?

Answer 8

Remember that a body will move in a straight line unless acted upon by a resultant acceleration as described by Newtons law of inertia

Question 9

State the equation for calculating radial acceleration

Answer 9

a_r = v² / r

OR a_r = r ω²

• ar = radial acceleration
• v = linear velocity
• r = radius
• ω = angular velocity

Question 10

Do worked example pg. 30 forces unit in binder

Question 11

Do SAQ 18

Answer 11

Ans in workbook

Question 12

What is the inertia of a rotating body called?

Answer 12

The moment of inertia

Question 13

Describe how the inertia of a rotating body differs to the inertia of a body moving in a straight line

Answer 13

• It is dependent on the body’s mass and how that mass is distributed within the body itself in relation to the axis of rotation
• Whereas the inertia of a body moving in a straight line is just dependent on its mass

Question 14

What is the formal definition of the moment of inertia ?

Answer 14

The sum of the products of the mass of each particile of the body and the square of its perpendicular distance from the axis of rotation

Question 15

Consider two wheels of equal mass rotating about an axis going straight through the centre of the wheel, one wheel is hallow with its mass distributed further from its axis of rotation what will this mean with regards to the moment of inertia of the hollow wheel and the ease of acceleration of it compared to the other wheel?

Answer 15

The hollow wheels moment of inertia will be greater, making it harder to accelerate (refer to pg. 32 forces unit in binder)

Question 16

State the equation for calculating the applied moment using moment of inertia and angular acceleration and also state the equation this is similar to

Answer 16

M = I α

• M = applied moment (tendency of a force to produce a rotation)
• I = moment of inertia
• α = angular acceleration

This is similar to F = ma

Question 17

State the equation for calculating the moment of inertia

Answer 17

I = m r²

• I = the moment of inertia
• m = mass
• r = radius (position of the mass relative to the axis of rotation)

Question 18

For an actual body what will the momeant of inertia be equal to ?

Answer 18

It will be equal to the sum of all the individual moments of inertia of each of its component parts

Equation is on pg 32. binder forces unit as i cannot put it in this

Consider a wheelchair wheel. It is made up of its hub, spokes, rim and tyres (Fig. 37 pg. 33 forces unit). The total moment of inertia of the wheelchair wheel is the sum of the moment of inertia of its component parts thus:

I_WHEEL = I_HUB + (N_SPOKESI_SPOKE) + I_RIM + I_TYRE

N spokes is because there is numerous spokes if you look at the pic

Question 19

Do SAQ 19

Answer 19

Ans in workbook

Question 20

What is the difference in how you should consider the centre of mass of a body to be concentrated at in rotary motion compared to linear motion ?

Answer 20

When considering linear motion we think of all the mass of a body to be concentrated at its centre of mass

Whereas when considering rotary motion, it is useful to think of all the mass of a body as being concentrated at a particular radius from the axis of rotation. This radius is termed the radius of gyration of the body

Question 21

What is the symbol and units for radius of gyration?

Answer 21

• Smybol = k
• Units = metres (m)

Question 22

Using the radius of gyration of a body what equation can be used for calculating the moment of inertia of a body undergoing rotary motion?

Answer 22

I = m k²

• I = the moment of inertia
• m = mass
• k = radius of gyration

Think about the example of the wheelchair wheel. The wheel can be represented by a body with all its mass concentrated at its radius of gyration, k_WHEEL (refer to pic on pg. 34 forces unit)

Question 23

For a solid ring or a spoked wheel what is the radius of gyration equal to?

Answer 23

k = r

• Remember that the radius of gyration is the radius from the axis of rotation where all the mass of a body undergoing rotary motion can be thought to be concentrated at
• Whereas r = the position of the mass relative to the axis of rotation

Question 24

For a solid disk what is the radius of gyration equal to ?

Answer 24

k² = 1/2(r)²

• Remember that the radius of gyration is the radius from the axis of rotation where all the mass of a body undergoing rotary motion can be thought to be concentrated at
• Whereas r = the position of the mass relative to the axis of rotation

Question 25

Do SAQ 20

Answer 25

Ans in workbook

Question 26

Describe what 2 things angular momentum incorporates ?

Answer 26

It incorporates a body’s resistance to change its rotary motion (moment of inertia) and ita angular velocity

This is similar to linear momentum = mass x linear velocity

Question 27

State the equation for calculating angular momentum

Answer 27

L = I ω

• L = angular momentum
• I = the moment of inertia
• ω = angular velocity

Question 28

What type of quantity is angular momentum?

Answer 28

It is a vector quantity, acting along the same axis as the angular velocity

Question 29

What are the SI units of angular momentum ?

Answer 29

(kilogram metres squared radian per second) kg m² rad s^-1

Question 30

Is the principle of conservation of momentum also applicable to angular momentum?

Answer 30

Yes

Question 31

Do SAQ 21 pg. 34 forces unit

Answer 31

Ans in workbook

Question 32

Define what antropometry is

Answer 32

This is the study of the human size and form

Question 33

Why in biomechanics is standardised sets of anthropometric data often used ?

Answer 33

Because it is often too difficult and too time consuming to measure all the required antropoemetric characteristics of each and every subject.

Question 34

In biomechanics what antropometric data is of most importance and why ?

Answer 34

Body segment parameters - this is because body segment parameters describe the mechanical attributes of a body segment which are required to solve biomechanical problems

Question 35

What are the 4 basic body segment parameters needed to solve basic biomechanical problems?

Answer 35

1. Length
2. Mass
3. Centre of mass
4. Radius of gyration

Question 36

Along with the 4 basic body segment parametres what is the 5th body segment parametre that may be considered and why ?

Answer 36

The origin and insertion sites of the active muscles - this is if the actions of the muscles are also to be included in biomechanical analysis

Question 37

Using standardised antropometric data how is the length of a persons body segments estimated from their height?

Answer 37

The length of each body segment is expressed as a ratio of body height (H), it is then easy to calculate an estimate for the length of a particular segment if the patients height is known.

Question 38

What do body dimensions between individuals vary due to ?

Answer 38

• Age
• Body build
• Sex
• Racial origin

Question 39

What is the most accurate way of obtaining body segment length?

Answer 39

Direct measurment

Question 40

When should standardised data sets for body segment lengths be used?

Answer 40

Only when it is not possible to make direct measurments

Question 41

Do worked example and SAQ 20 on pg. 36

Answer 41

Ans in workbook

Question 42

Standardised data sets for the mass and the position of the centre of mass of each body segment have also been produced, this is because both of these cannot be easily measured

These data sets may take several different forms, each requiring different types and amounts of information e.g. some require skin fold measurements and the simplest require only the total body mass of the subject and length of each segment

How are these data sets often presented ?

Answer 42

The coefficients are in the form of ratios of segment mass to whole body mass and centre of mass to segment length

• e.g. segment mass to total body mass - 0.006 for hand
• e.g. centre of mass to segment length - promximally: 0.560 (of the total segment length from the proximal end) and distally: 0.494

Refer to fig. 41 on pg. 37

Question 43

Why is the position of each centre of mass in each body segment closer to the proximal segment than the distal?

Answer 43

Because in general the diameter of each segment increases towards the proximal end

Question 44

Do worked example and SAQ 23 on pg. 37

Answer 44

Ans in workbook

Question 45

Does a rotating body have inertia similar to that of a body moving in a straight line?

Answer 45

Yes - the inertia of a rotating body is called the moment of inertia

Question 46

Considering the definition for moment of inertia how does the distance the mass of the body is concentrated at in relation to the axis it is rotating about affect the moment of inertia ?

Answer 46

As the distance the mass is concentrated at from the axis it is rotating about increases the moment of inertia also increases

Question 47

What symbol is used to represent the moment of inertia and what are its SI units ?

Answer 47

Moment of inertia = ɪ

SI units = kg m^-2