Flashcards in Unit 5: Rotational dynamics Deck (58)

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1

## What are angles and angular displacements measured in?

### Radians

2

## What is the definition of a radian?

### When the arc length is equal to the radius, the angle θ is equal to one radian

3

## What is the formula for angular velocity?

### ω = Δθ/Δt rad(s^-1)

4

## What is the formula for velocity in terms of angular velocity?

### v = rω

5

## When does angular acceleration arise?

### When a particle increases its speed of rotation

6

## What is angular acceleration defined as?

### The rate of change of angular velocity

7

## What is the formula for angular acceleration?

### α = Δω/Δt rad(s^-2)

8

## What must an increase in angular acceleration be accompanied by?

### A corresponding increase in the tangential acceleration

9

## What is the formula for tangential acceleration in terms of angular acceleration?

### a = rα

10

## What do the dynamics involving movement about a circle assume?

### It considers a body that can be treated as a single particle where all the mass is centred at a point but this simplistic assumption cannot be made in more realistic situations

11

## What does the dynamics of a rotating body depend upon?

### The distribution of the mass of the body in relation to a particular axis of rotation

12

## What is a body composed of?

### An infinite number of point masses (or elemental particles) that move collectively - each point mass within the body will have a different radius from the axis of rotation and will therefore rotate with a different tangential velocity

13

## What does inertia mean?

### The resistance of an object to a change in its motion

14

## What is the formula for the moment of inertia?

### I = Σm(r^2)

15

## What are the units of the moment of inertia?

### kg(m^2)

16

## When is the summation for the moment of inertia replaced by integration?

### In the case of a rigid body with a mass that is continuous

17

## What affects the value of the moment of inertia?

### The precise location of the axis of rotation

18

## What increases the moment of inertia?

### Distributing the mass further from the centre of rotation

19

## What is the moment of inertia of a hoop about the central axis?

### I = M(R^2)

20

## What is the moment of inertia of a solid sphere about any diameter?

### I = 0.4M(R^2)

21

## What is the moment of inertia of a solid cylinder/disc about the central axis?

### I = 0.5M(R^2)

22

## What happens to the moments of inertia of two objects that share a common axis of rotation?

### Their individual moments of inertia are added together to give a moment of inertia for the combined system

23

## What is a flywheel?

### A mechanical device with a large moment of inertia that stores rotational energy

24

## What is the formula for rotational kinetic energy?

### Ek = 0.5I(ω^2)

25

## When a body is rotating about a centre of rotation, what does it possess energy due to?

### Its rotational movement

26

## What are the four rotational equations of motion?

### ω2 = ω1 + αt, θ = ω1t + 0.5α(t^2), (ω2)^2 = (ω1)^2 + 2αθ and θ = 0.5(ω1 + ω2)/t

27

## What is torque?

### The moment (or turning effect) of a force about a point

28

## What is the definition of torque?

### A torque is the product of a force and the perpendicular distance of the line of action of the force from a perpendicular point of rotation. The unit of torque is newton metre (Nm). The convention adopted is that positive torques produce a clockwise rotation

29

## What is the formula for torque in terms of force?

### T = Fs

30