## Course Description

### Overview

This course is targeted at Singapore Cambridge GCE O level students, but is also relevant to IGCSE students and Singapore's Integrated program students.

If you've been following our course on forces, you should be familiar with how forces make objects move from place to place. But that's not all forces do. Ask anyone who's thrown a shuriken before and they'll tell you that the force you exert on it also causes it to spin. In fact, we use this turning effect from forces in levers, winches and the wheel and axle to make life easier for ourselves. So if you're interested to find out what forces have to do with spinning objects, this course is the one you want to take.

### Course Content

You will learn:

• Why the shuriken spins
• How to calculate torque
• What the centre of gravity is and how to find it
• How to determine whether and object is going to topple or not
• The principle behind those balancing toys that just don't seem to fall down
• Other cool stuff! (Some of the videos in this course are marked as "explanation videos", which go into greater depth on the topics covered. We try to bring in out-of-syllabus concepts where possible to make things more interesting and give a more complete understanding of the topic)

A link to the full O level Physics syllabus can be found here

### Course Prerequisites

You will need to know:

• Some knowledge of forces (how to split a force into different components)
• How to watch videos on your computer Math Arena

The instructor is from Math Arena.The instructor is absolutely passionate about teaching and you'll find the lessons engaging and ultimately rewarding.

## Course curriculum

• 1

### Introduction

• Subject Content Requirements

• 2

### Basic force diagram

• Q1 Two blocks are placed on a beam which balances on a pivot at its centre. The weight of the beam is negligible. Which diagram shows the forces acting on the beam?

• 3

### Calculating moments

• Q2 A horizontal pole is attached to the side of a building. What is the moment of the force F about the pivot P?

• Q2 explanation

• Q3 A wooden bar is pivoted at its centre so that it can rotate freely. Two equal forces F are applied to the bar. In which diagram is the turning effect the greatest?

• Q4 The figure below shows the same vertical force of 200 N exerted by a cyclist on the pedal of a bicycle in three different positions A, B, and C. State the position, A, B or C, in which the force exerts the largest moment about the pivot.

• Q5 In order to open a door, a minimum moment of 31.2 Nm is needed. What is the minimum distance of the handle from the hinges, if the door is to be pulled open with a force at the handle not higher than 60 N?

• Q5 explanation

• Q6 Three forces of magnitude 14 N, 16 N and 30 N are applied on a wheel as shown. Which of the statements regarding resultant force and resultant moment are correct?

• 4

### Balancing clockwise and anticlockwise moments

• Q7 What are the conditions for equilibrium?

• Q8 The diagram shows an unbalanced rod. Two loads X and Y can be moved along the rod. The rod turns in a clockwise direction as shown. Which action could make the rod balance?

• Q9 Which equation relating to W, Z, a and b is correct?

• Q10 The diagram shows a wheelbarrow and its load, which have a total weight of 150 N. This is supported by a vertical force F at the ends of the handles. What is the value of F?

• Q10 explanation

• Q11 The total weight of the load and the wheelbarrow shown is 600N. What is the size of force F needed just to lift the loaded wheelbarrow?

• Q11 explanation

• Q12 A man uses a metal rod to raise a large stone as shown below. Which force would raise the large stone most easily?

• Q13 A windmill is pushed by four external forces as shown. Calculate Force F required to make the windmill stand still.

• 5

### More complex equilibria

• Q14 A driver’s foot presses with a steady force of 20 N on a pedal in a car as shown.What is the force F pulling on the piston?

• Q14 explanation

• Q15 When the forcemeter A was used on its own on the spanner to loosen a nut it read 200 N. Forcemeter B was then used on its own to loosen the nut and it read 300 N. What was the distance X in the diagram?

• Q16 The centre of a bridge was broken in a storm. A man of mass 100 kg tries to go to the other side, but after 10 m, the bridge starts to creak and he has to return. A boy tried to do the same, and just manages to jump over. What is the boy mass in kg?

• Q17 A 1 m long uniform beam is being balanced as shown below. Calculate force G.

• 6

### Introduction to the centre of gravity

• Q18 A 1 m long uniform beam of 6 N weight is being lifted up vertically by a force F at the 75 cm mark. What is the minimum force to do so?

• Q19 The diagram below shows a man of weight 800 N standing in the middle of a uniform, rigid, horizontal plank. The plank weighs 1000 N. Which one of the following diagrams shows the forces on the plank?

• Q20 The below shows a non-uniform tree trunk of weight 1000 N resting horizontally on two supports at Q and S. The centre of mass of the tree trunk is at R. What downward force must be applied at P to lift the tree trunk just clear of the support at S?

• Q21 A boy who weighs 500 N stands on a uniform plank with supports at P and Q. What are the upward forces acting on the plank at P and Q?

• Q22 A thin uniform sheet of metal is cut into an irregular shape. It is 400 mm long, weighs 5 N and is hung at point P, halfway along it. The 3 N weight hung at Y makes it balance as shown. How far from P is its centre of gravity?

• Q23 A uniform metre rod of weight 10 N leans against a smooth glass door in an equilibrium position as shown. What is the reaction force of the glass door on the rod?

• Q24 A plane lamina is freely suspended from point P. The weight of the lamina is 2.0 N and the centre of mass is at C. The lamina is displaced to the position shown. What is the moment that will cause the lamina to swing?

• Q25 A trap door XY of length 1.00 m and weighing 30 N is hinged at the end X. It is opened by pulling a string inclined at an angle 40° to the horizontal. What is the tension T in the string required to just lift the trap door?

• Q24 explanation

• Q26 A square shop sign (of side 1 m) consisting of a uniform lamina PQRS is attached to a vertical wall by a hinge at P so that S rests against the wall vertically below P. If the mass of the sign is 5 kg and normal reaction exerted by the wall at S is

• Q27 A horizontal force F is applied to a cylinder weighing 100 N as shown below. Given that the radius of the cylinder is 0.5 m, what is the smallest value of F to cause the cylinder to roll up the step?

• Q28 A square metal sheet has the corner (shaded) cut off. Which point will be nearest to the centre of gravity of the new sheet?

• 7

### Stability and the centre of gravity

• Q29 Four table lamps are shown along with the position M of the centre of mass in each case. Which lamp is the most stable?

• Q30 The diagram shows sections of four objects of equal mass. The position of the centre of mass of each object has been marked with a cross. Which object is the most stable?

• Q31 Some containers are made from thin glass. Which empty container is the most stable?

• Q32 The diagram shows four objects standing on a flat surface. The centre of mass of each object is marked M. Which object will fall over?

• Q32 explanation

• Q33 An empty glass is placed on a join between two tables as shown. The glass remains stable. Which point is the centre of mass of the glass?

• Q34 Books are placed in four bookcases as shown. Which bookcase is most likely to fall forward if pulled a little?

• Q35 The figure below shows a a triangular prism. G is the centre of mass. The prism is laid on one of its rectangular faces. On which side, PO or QR or RP, should it be placed for maximum stability?

• Q35 explanation

• Q36 A light aircraft stands at rest on the ground. It stands on three wheels, one at the front and two further back. Which point could be its centre of mass?

• Q37 A tractor is being used on rough ground. What is the safest position for its centre of mass?

• Q38 A girl uses paper-clips to balance a toy bird on her finger as shown. What is the effect of the paper-clips?

• 8

### Lamina questions

• Q39 A piece of card has its centre of mass at M. Which diagram shows how it hangs when suspended by a thread?

• Q40 A piece of uniform card is suspended freely from a horizontal pin. At which of the points shown is its centre of gravity?

• Q41 The diagram shows a flat metal plate that may be hung from a nail so that it can rotate about any of four holes. What is the smallest number of holes from which the flat metal plate should be hung in order to find its centre of gravity?

• Q42 The centre of mass of the lamina in the diagram is at B. A disc is then attached as shown. Which letter shows a possible position of the centre of mass of the lamina-disc combination?

• 9

### Structured Questions

• SQ1 Tumbling Kelly

• SQ2 Balancing toy

• SQ3 Turning moment of force at an angle

• SQ4 (part 1) Spanner question definition of moment

• SQ4 (part 2) Spanner question calculating force and moment

• SQ5 (part 1) Twin-bladed helicopter mass of helicopter

• SQ5 (part 2) Twin-bladed helicopter lift force from rotors

• SQ5 (part 3) Twin-bladed helicopter tilting the copter

• SQ6 Rolling a ball up a step

• SQ7 (part 1) Windsurfer pulling up the sail

• SQ7 (part 2) Windsurfer calculating moments in equilibrium

• SQ7 (part 3) Windsurfer learning outwards for stability

• SQ8 (part 1) Water park tipping can stability

• SQ8 (part 2) Water park tipping can pivot point

• SQ10 (part 1) Winch calculating tension

• SQ10 (part 2) Winch why is the force reduced

• SQ9 Gym machine

• SQ11 Hydrogen balloon

• SQ12 Airport trolley

• SQ13 Bicep curl

• SQ14 Levering the stone slab