Engineering Physics- PART 1

Question 1

What properties does a rigid rotating body have?

Answer 1

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

These properties can be inferred from the properties of objects moving in a straight line combined with the geometry of circles and arcs

Question 2

Define angular displacement

Answer 2

The change in angle through which a rigid body has rotated relative to a fixed point

Angular displacement is measured in radians

Question 3

How can the linear displacement s at any point along a segment that is in rotation be calculated?

Answer 3

Where:

θ = angular displacement, or change in angle (radians)

s = length of the arc, or the linear distance travelled along a circular path (m)

r = radius of a circular path, or distance from the axis of rotation (m)
[NOT GIVEN]

Question 4

Draw a circle with annotations

Answer 4

An angle in radians, subtended at the centre of a circle, is the arc length divided by the radius of the circle

Question 5

Define the angular velocity ω of a rigid rotating body?

Answer 5

The rate of change in angular displacement with respect to time

Angular velocity is measured in rad s^–1

Question 6

What is the equation for angular velocity?

Answer 6

[NOT GIVEN]

Question 7

The linear speed v is related to the angular speed ω by what equation?

Answer 7

[NOT GIVEN]

Question 8

Taking the angular displacement of a complete cycle as 2π, angular velocity ω can also be expressed as what equation?

Answer 8

[NOT GIVEN]

Question 9

Define angular acceleration α

Answer 9

The rate of change of angular velocity with time

Angular acceleration is measured in rad s^−2

Question 10

What is the equation for angular acceleration?

Answer 10

[NOT GIVEN]

Question 11

Using the definition of angular velocity ω with the equation for angular acceleration α gives…

Answer 11

[NOT GIVEN]

Question 12

Rearranging gives the expression for linear acceleration, which is?

Answer 12

[NOT GIVEN]

Question 13

TIPP!!!!

Answer 13

While there are many similarities between the angular quantities used in this topic and the angular quantities used in the circular motion topic, make sure you are clear on the distinctions between the two, for example, angular acceleration and centripetal acceleration are not the same thing!

Question 14

How can the graphs of rotational motion be interpreted?

Answer 14

in the same way as linear motion graphs

Question 15

Draw the graphs of angular displacement, angular velocity and angular acceleration?

Answer 15

Question 16

What is angular displacement θ, is equal to…

Answer 16

The area under the angular velocity-time graph

Question 17

What is angular velocity ω equal to?

Answer 17

The gradient of the angular displacement-time graph

The area under the angular acceleration-time graph

Question 18

What is angular acceleration α equal to?

Answer 18

The gradient of the angular velocity-time graph

Question 19

Create a summary table of linear and angular variables

Answer 19

Question 20

The kinematic equations of motion for uniform linear acceleration can also be re-written for rotational motion

What are the four kinematic equations for uniform linear acceleration?

Answer 20

[GIVEN]

Question 21

What are the four kinematic equations for uniform rotational acceleration?

Answer 21

[GIVEN]

Question 22

Draw a table of the linear variables and their rotational equivalents

Answer 22

Question 23

Define torque

Answer 23

The change in rotational motion due to a turning force is called torque

Question 24

What is the equation for The torque of a force F about an axis?

Answer 24

[GIVEN]

Question 25

How can the torque applied by a cyclist on a bicycle pedal be determined?

Answer 25

using the magnitude of the applied force, from the cyclist, and the distance between the line of action of the force and the axis of rotation, the length of the crank arm r

Question 26

When applied to a couple (2 forces), torque can be described as:

Answer 26

The sum of the moments produced by each of the forces in the couple

Question 27

What is the equation of a torque provided by a couple on a steering wheel of radius r?

Answer 27

τ = (F x r) + (F x r) = 2Fr [NOT GIVEN]

Question 28

Is the torque of a couple on a steering wheel in rotational equilibrium?

Answer 28

The steering wheel is in rotational equilibrium since the resultant force and resultant torque are zero. This means it does not have linear or angular acceleration. For example, the torque provided by a couple on a steering wheel of radius r is τ = (F x r) + (F x r) = 2Fr [NOT GIVEN] Therefore, the torque of a couple is equal to double the magnitude of the torque of the individual forces The forces are equal and act in opposite directions Therefore, couples produce a resultant force of zero Due to Newton’s Second law (F = ma), the steering wheel does not accelerate In other words, when the force is applied, the steering wheel rotates with a constant angular speed but remains in the same location

Question 29

TIPP!!!

Answer 29

The terminology in this section can get confusing. For example, a moment is not a 'turning force' - the turning force is only part of the moment, the moment is the effect that the turning force has on the system when applied at a distance from a turning point, or pivot. This is often linked with content from the moments section of the course. Ultimately, when you carry out calculations, make sure you can identify The magnitude of the applied force The perpendicular distance between the force and the turning point (along the line of action) When considering an object in rotational equilibrium, choosing certain points can simplify calculations of resultant torque. Remember you can choose any point, not just the axis of rotation. To simplify your calculation, choose a point where the torque of (most of) the forces are unknown, or when you need to determine where the resultant torque is zero. To do this, choose a point through which the lines of action of the forces pass.

Question 30

What is inertia?

Answer 30

In linear motion, the resistance to a change of motion, i.e. linear acceleration, is known as inertia The larger the mass an object has, the greater its inertia

Question 31

What is the the rotational equivalent of mass?

Answer 31

In rotational motion, the distribution of mass around an axis must be considered, using moments of inertia

Question 32

Define the moment of inertia of a rigid, extended body

Answer 32

The resistance to a change of rotational motion, depending on the distribution of mass around a chosen axis of rotation Moment of inertia is measured in kg m^2

Question 33

The moment of inertia of a body corresponds to how 'easy' or 'hard' it is to rotate, and this is dependent on many factors, including...

Answer 33

1) The total mass (m) 2) How its mass is distributed about the axis of rotation (r) For example, if a springboard diver jumps off a board and does a flip, they tuck their legs closer to their chest. This decreases their moment of inertia, as more of their mass is distributed over a smaller distance. This makes it easier for them to rotate

Question 34

What does the change in the moment of inertia of a diver look like?

Answer 34

The distance from the axis of rotation changes as the diver curls up and straightens out again

Question 35

How can the moment of inertia of a singular object can change?

Answer 35

It can change depending on its orientation in relation to the chosen axis of rotation For example, the moment of inertia of a thin rod is different for each of the following orientations: Rotation about its vertical axis Rotation about its centre of mass Rotation about one end

Question 36

The moment of inertia of a body can change depending on what?

Answer 36

its orientation relative to the axis of rotation

Question 37

Different orientations of a thin rod have different moments of inertia, what are they?

Answer 37

These are just a few of the possible orientations of the axis of rotation for a thin rod There is an infinite range of possible axes, and therefore an infinite possible set of values for the moments of inertia This also applies to nearly all rigid, extended objects that could be considered

Question 38

The moment of inertia of a point mass is equal to what?

Answer 38

[GIVEN]

Question 39

What is the moment of inertia for an extended object about an axis?

Answer 39

it is defined as the summation of the mass × radius2 for all the particles that make up the body

Question 40

TIPPS!!!

Answer 40

You will never be expected to memorise the moments of inertia of different shapes, they will always be given in an exam question where required