Mechanics/ biomechanics - unit 1 deck 2

Question 1

Refer to figures 21 & 22 in binder to see the independent 3 translations and 3 rotations

Question 2

What is each translation and each rotation defined as ?

Answer 2

A degree of freedom

Question 3

How many degrees of freedom does an object which is free to move in all directions said to have ?

Answer 3

six degrees of freedom

Question 4

The 6 different degrees of freedom are independent of eachother - T/F and explain ans

Answer 4

True - this is because the x, y, z axes are at right-angles to eachother

Question 5

Refer to fig 23 of the binder to help get your head around rotatory degrees of freedom

Question 6

Define what linear motion is

Answer 6

This is motion in a straight line

Question 7

What are the 4 parameters used to describe linear motion ?

Answer 7

1. Time
2. Displacement
3. Linear velocity
4. Linear acceleration

Question 8

What is the difference between speed and velocity?

Answer 8

• Speed is the rate of change of distance travelled i.e. distance travelled divided by time
• Whereas velocity is the rate of change of displacement i.e. speed and direction of travel ==> it is a vector quantity

Question 9

What are the SI units of velocity ?

Answer 9

m s^-1 - metres per second

Question 10

What are the 2 types of velocity that we are concerned with ?

Answer 10

1. Average velocity - this is the displacement travelled divided by the time taken (note how its the displacement not distance because velocity is concerned with direction as well)
2. Instantaneous velocity - this is the velocity at an instant in time

Question 11

What is the equation for average velocity?

Answer 11

average velocity = change in displacement/ time taken

v = Δs / t OR v = s - s_o / t

• v = velocity
• Δs = change in displacement
• t = time taken for the change to occur
• s = the final displacement relative to a reference point
• s_o = the original/ initial displacement relative to a reference point

Question 12

How should a displacement-time graph be plotted and what are they used to calculate ?

Answer 12

It should be plotted with time on the x-axis and displacement on the y-axis

These graphs are used to calculate velocity

Question 13

How is the gradient of a straight line calculated ?

Answer 13

For a straight-line graph, pick two points on the graph. The gradient of the line = (change in y-coordinate)/(change in x-coordinate)

Question 14

What can be stated in general is the relevance of the gradient of a displacement-time graph ?

Answer 14

The gradient of a displacement-time graph is the velocity

It is useful to refer to and read over pages 19&20 in the binder

Question 15

How is the instantaneous velocity calculated on a displacement-time graph if the graph is curved ? (like in figure 25 page 20 in the binder)

Answer 15

You can calculate it by drawing a tangent to the curve at a particular point, you then basically use the numbers from the plotted points immediately before and after the point on the graph you want to calculate the instantaneous velocity for.

Refer to fig.26 on pg.20 in the binder for visual explanation

Question 16

Define acceleration

Answer 16

It is the rate of change of velocity

e.g. a car starting from rest, it must build up its velocity from 0 to say 50 km per hour. To do so it must accelerate

It is a vector quantity

Question 17

What are the SI units of acceleration ?

Answer 17

m s^-2 - meters per second squared

Question 18

Define average acceleration and instantaneous acceleration

Answer 18

1. Average acceleration is the change in velocity divided by the time taken
2. Instantaneous acceleration is the acceleration at an instant in time

Question 19

What is the equation used to calculate average acceleration?

Answer 19

acceleration = change in velocity/ time taken

a = Δv / t OR a = v - v₀ / t

• a = acceleration
• Δv = the change in velocity
• t = the time taken for the change to occur
• v = the final velocity
• v₀ = the initial velocity

Question 20

How should a velocity-time graph be plotted and what are they used to calculate ?

Answer 20

Should be plotted with time on the x-axis and velocity on the y-axis

They are used to calculate acceleration

Refer to fig.27 on pg.21 in binder

Question 21

How is the gradient of a velocity-time graph calculated and what does the graident repesent ?

Answer 21

The gradient is calculated the exact same way as in displacement-time graphs depending on if it is a striaght or curved line

The gradient (velocity/ time taken) in this graph represents the acceleration

Question 22

When does deceleration occur ?

Answer 22

This occurs when an object is slowing down, during deceleration the calculated acceleration is negative since the change in velocity will be negative

Question 23

What is the difference between the value you would get if an object is deccelerating rather than accelerating ?

Answer 23

You would calculate it the same way but a decceleration would give out a negative number since the change in velocity will be negative, whereas acceleration the value will be positive

Question 24

Describe rotary motion

Answer 24

This is when an object can be rotating about a point on itself e.g. an ice skater performing a spin

OR when an object is rotating around an external fixed point e.g. a gymnast swining on a horizontal bar as shown in fig.28

Question 25

What are the 4 parameters needed to describe rotary motion ?

Answer 25

1. Time 2. Angular displacement 3. Angular acceleration 4. Angular velocity

Question 26

What are the following greek symbols used to represent ? * α - alpha * ω - omega

Answer 26

* α; alpha - represents angular acceleration * ω; omega - represents angular velocity

Question 27

A rotating object has an angular velocity, define what this is

Answer 27

This is the angular displacement travelled per second

Question 28

What are both angular displacement and angular velocity ?

Answer 28

They are both vector quantities

Question 29

What are the 3 important things to remember to specify when using angular velocity ?

Answer 29

1. The mangnitude 2. The axis about which it rotates 3. The direction of rotation

Question 30

What are the two different types of angular velocity which can be calculated and state their definitions

Answer 30

1. Average angular displacement = the angular displacement divided by the time taken 2. Instantaneous angular velocity = the angular velocity at an instant in time

Question 31

State the equation for calculating the average angular velocity

Answer 31

Average angular velocity = change in angular displacement / time taken OR ω = Δθ / t OR ω = θ - θ_o / t * ω = angular velocity * Δθ = change in angular displacement * θ = final angular displacement * θ_o = initial angular displacement * t = time taken

Question 32

What are the SI units of angular velocity ?

Answer 32

radians per second (rad s^-1)

Question 33

Other than the equations what can be done to calculate the angular velocity ?

Answer 33

Plot an angular displacement-time graph

Question 34

When plotting an angle-time graph what it labelled as the x and y axes ?

Answer 34

* X axis is the time taken * Y axis is the angular displacement

Question 35

How is the angular velocity calculated using an angle-time graph?

Answer 35

The gradient calculated to give the angular velocity For instantaneous velocity a tangent to the curve can be drawn and then the gradient calculated using trigonometry (i.e. using the 2 immediate points before and after like in the other graphs)

Question 36

Refer to pg. 23 for SAQ 13 which gives practice on plotting an angle time graph

Question 37

Define what the angular acceleration of a rotating object is

Answer 37

This is the rate of change of angular velocity e.g. the wheels of a car accelerating from rest will undergo angular acceleration (in the z axis)

Question 38

What are the SI units of angular acceleration?

Answer 38

radians per second squared (rad s^-2)

Question 39

What are the two methods for calculating angular acceleration?

Answer 39

Via equations or via an angular velocity-time graph

Question 40

What is the gradient of an angular velocity-time graph equal to ?

Answer 40

The angular acceleration Average and instantaneous angular acceleration is calcuated the same way as when using any of the other graphs

Question 41

Define both average and instantaneous angular acceleration

Answer 41

Average angular acceleration = the change in angular velocity divided by the time taken Instantaneous angular acceleration = the angular acceleration at an instant in time

Question 42

State the equation for calculating average angular acceleration

Answer 42

Average angular acceleration = change in angular velocity / time taken OR α = Δω / t OR α = ω - ω_o / t * α = angular acceleration * Δω = the change in angular acceleration * ω = final angular velocity * ω_o = initial angular velocity * t = time taken

Question 43

Do the worked example and SAQ 14 for calculating angular acceleration