Rotational Dynamics

Question 1

Define inertia

Answer 1

An objects resistance to a change in velocity when subjected to a force

Question 2

What does a large inertia mean

Answer 2

Large force required to change velocity

Question 3

Define moment of inertia

Answer 3

An objects resistance to being rotationally accelerated about an axis

Question 4

What is the equation for inertia for a point mass

Answer 4

I = m r^2

Question 5

What is r in the inertia equation

Answer 5

Distance from the axis of rotation

Question 6

Define an extended object

Answer 6

Has more than 1 point mass

Question 7

What is the inertia equation for an extended object

Answer 7

I = sum (mr^2)

Question 8

What are 2 factors that affect an objects moment of inertia

Answer 8

1) the objects mass

2) how its mass is distributed about the axis of rotation

Question 9

How does an objects mass distribution vary

Answer 9

Varies when distance from axis of rotation varies

Question 10

How do you calculate the moment of inertia of a system

Answer 10

Sum of individual objects moment of inertia that make up the system

Question 11

How do you calculate a new moment of inertia

Answer 11

I new = I + mr^e

Where i is the original moment of inertia

Question 12

What is the equation for rotational kinetic energy

Answer 12

Ke = 1/2 I w^2

Question 13

What is a flywheel

Answer 13

A large heavy disc with a very large moment of inertia

Question 14

What does a flywheel having a large moment of inertia mean

Answer 14

It requires a strong force to relationally accelerate it but doesn’t stop spinning when started

Question 15

How does a flywheel work

Answer 15

Input torque is transferred into rotational kinetic energy which is stored in the flywheel

Question 16

What are 4 factors that affect the ke stored by a flywheel

Answer 16

1) angular speed

2) mass of flywheel

3) friction

4) spoked flywheel

Question 17

How does angular speed affect ke stored by flywheel

Answer 17

Ke is directly proportional to the square of angular speed

Question 18

How does mass of flywheel affect the ke stored

Answer 18

Larger mass mean larger moment of inertia so larger ke as ke is directly proportional to I

Question 19

How can you reduce friction in a flywheel

Answer 19

• lubricate bearings
• use in a vacuum to reduce air resistance
• use superconductor bearings so flywheel levitates

Question 20

How does smoking a flywheel affect the ke stored

Answer 20

Increases it as mass is distributed further from the axis of rotation so moment of inertia is greater

Question 21

What are 4 uses of flywheel

Answer 21

1) regenerative braking in vehicles

2) wind turbines

3) smooth torque/ angular velocity

4) production processes

Question 22

Describe regenerative braking

Answer 22

When brakes are applied, flywheel is engaged and uses energy lost by braking to charge

Question 23

Describe how flywheels are used in wind power

Answer 23

Store excess power for unwind days

Question 24

Describe how flywheels can produce smooth torque

Answer 24

If torque supplies fluctuates, flywheels charge with bursts of energy and output it smoothly to system

Question 25

What happens to flywheel if force increases

Answer 25

Flywheel decelerates to output energy

Question 26

What happens to flywheel if force required decreases

Answer 26

Flywheel accelerates to store excess energy

Question 27

Describe production processes

Answer 27

They rely on repeating actions where a large amount of power must be output in a short time

Question 28

How do flywheel help production processes

Answer 28

Electric motor charges flywheel which then transfers energy, so stops motor stalling due to large changes in power and means you can use a less powerful motor

Question 29

Define angular displacement

Answer 29

Angle turned through, radians

Question 30

Define angular speed

Answer 30

Angle turned through per unit time, rad s -1

Question 31

Define angular velocity

Answer 31

Angle turned through, clockwise or anti-clockwise per unit time, rad s -1

Question 32

Define angular acceleration

Answer 32

Change in angular velocity per unit time, rad s -2

Question 33

What does the area under an acceleration - time graph represent

Answer 33

Angular velocity

Question 34

What does the gradient of a angular velocity - time graph represent

Answer 34

Angular acceleration

Question 35

What is the relationship between angular displacement and time

Answer 35

Angular displacement is proportional to t^2

Question 36

Define torque

Answer 36

Torque is the product of force x distance from axis of rotaiton

Question 37

What does torque cause

Answer 37

Angular acceleration

Question 38

What is the equation for torque

Answer 38

T = F r

Question 39

Give 2 ways to increase Angular acceleration

Answer 39

1) increase m to increase torque 2) use a lighter wheel to decrease moment of inertia

Question 40

Give an equation for torque

Answer 40

T = I a

Question 41

Define angular momentum

Answer 41

Angular momentum is the product of moment of inertia and angular velocity

Question 42

Give an equation for angular momentum

Answer 42

Angular momentum = I w

Question 43

What is the law of conservation of momentum

Answer 43

When no external torque acts, the angular momentum of a system remains constant

Question 44

Define angular impulse

Answer 44

Angular impulse is the product of torque and its duration, where the applies torque is equal to the change in angular momentum

Question 45

Give an equation for angular impulse

Answer 45

T t = I w

Question 46

What does the area under a torque - time graph represent

Answer 46

Change in angular momentum

Question 47

Define work done

Answer 47

Work done is the force causing a motion x distance travelled

Question 48

Equation for work done

Answer 48

W = T S

Question 49

What does an increase in work done cause

Answer 49

An increase in rotational kinetic energy if frictional torque is overcome

Question 50

What does the area under a torque - angular displacement graph represent

Answer 50

Work done

Question 51

What is the equation for power

Answer 51

P = T w

Question 52

How do you calculate frictional torque

Answer 52

1) Apply accelerating torque 2) remove torque and measure time to come to rest 3) deceleration = w2 - w1 / t 4) frictional torque = I a