What do these objects have in common? LO: Understand how things balance What do these objects have in common? Use moments worksheet in resources folder

Centre of Mass Understand what is meant by centre of mass ALL – Define the centre of mass MOST – be able to find the centre of mass of symmetrical objects SOME – Explain why objects are designed to have a low centre of mass KEYWORDS: centre of mass, line of symmetry

LO: Understand what is meant by centre of mass For all objects, their mass is spread out over the whole object. However, this is not useful to us as Physicists!

LO: Understand what is meant by centre of mass The centre of mass of an object is that point at which the mass may thought to be concentrated

Finding the centre of mass LO: Understand what is meant by centre of mass Finding the centre of mass The centre of mass of complicated objects can be incredibly difficult to find. However, for simple, symmetrical objects, the COM can be easily found!

Centre of mass of symmetrical objects LO: Understand what is meant by centre of mass Centre of mass of symmetrical objects The centre of mass of symmetrical objects ALWAYS lies along the line of symmetry of the object. Where the object has more than one line of symmetry, the COM will be at the point where the lines of symmetry intersect

LO: Understand what is meant by centre of mass Example 1 Indicate the region in which the centre of mass of the shape shown lies.

Show where the centre of mass of the shape shown lies. LO: Understand what is meant by centre of mass Example 2 Show where the centre of mass of the shape shown lies.

Note that this may not be possible for all of the shapes! LO: Understand what is meant by centre of mass Task Complete the work sheet to show where the centre of mass of the symmetrical objects are. Note that this may not be possible for all of the shapes!

LO: Understand what is meant by centre of mass Suspended objects If you suspend an object and then release it, it will soon come to a rest. When this happens, the centre of mass will be directly below the point of suspension. The object can be said to be in equilibrium. Demo

LO: Understand what is meant by centre of mass Irregular shapes The centre of mass of an irregular shape can be found by using the apparatus shown. The shape is hung from a point and a plumbline used to draw the region in which the COM lies. This is done repeatedly with the mass hung from different points. The point where all the lines intersect is the COM!

KNOWLEDGE CHECK C B A State what is meant by centre of mass Describe how you would find the centre of mass of a symmetrical object B Describe how you would find the centre of mass of an unsymmetrical object A

Stability Understand how to design stable objects Starter Challenge starter! Understand how to design stable objects ALL – state features of stable objects MOST – Explain what happens when objects topple over SOME – Evaluate the design of objects based on their stability KEYWORDS: centre of mass, stability, Moment, base, tractor

Keywords: Centre of mass Moment Pivot Base Topple

LO: understand how to design stable objects Although the design of cars has changed drastically over the last 100 years, a number of things have remained constant. Amongst them is to keep cars as low as possible. This means that the centre of mass of the car is low and it is less likely to topple over!

Why do objects tips over? LO: understand how to design stable objects Why do objects tips over? The weight of an object acts through the centre of mass. As the object is initially tilted, the weight is causing an anticlockwise moment about the pivot. If the object is let go, the moment will cause the object to go back onto its base.

Why do objects tips over? LO: understand how to design stable objects Why do objects tips over? As the object continues to be tilted, you will reach a point where the weight will go exactly through the pivot.

Why do objects tips over? LO: understand how to design stable objects Why do objects tips over? When the object has been tilted beyond a certain point, the weight will now cause a clockwise moment about the pivot. If the object is let go, the moment will cause the object to topple over!

The turning effect of a force is called a moment LO: Understand how things balance What is a moment? When the mass is placed on the left-hand side of the see-saw, it moves down. This is an anticlockwise turn The turning effect of a force is called a moment pivot

Moment = force x distance from pivot LO: Understand how things balance Calculating moments The moment of a force is calculated from: Moment = force x distance from pivot m = f x d Moment = Newton – Metres (Nm) Force = Newtons (N) Distance = metres (m)

LO: Understand how things balance Example 1 Gina weighs 500 N and stands on one end of a seesaw. She is 0.5 m from the pivot. What moment does she exert? moment = 500 x 0.5 = 250 Nm 0.5 m 500 N pivot

LO: Understand how things balance Example 2 If a force of 20 N presses down at a distance of 3 m from a pivot, its moment is: Moment = 20 N x 3 m = 60 Nm

LO: Understand how things balance Example 3 If a force of 30 N presses down at a distance of 4 m from a pivot, its moment is: Moment = 30 N x 4 m = 60 Nm

Right Hand Side of Pivot LO: Understand how things balance Calculating moments Left Hand Side of Pivot Right Hand Side of Pivot Mass (kg) Distance from pivot (m) Weight (N) Anticlockwise Moment (Nm) Clockwise Moment (Nm)   Remember: kg x 10 = N

Clockwise moments = anticlockwise moments LO: Understand how things balance Moments in balance A seesaw is an example of the principle of moments. This states that for an object in equilibrium (not moving!) the sum of all the clockwise moments about any point is equal to the sum of all the anticlockwise moments about the same point. Clockwise moments = anticlockwise moments W1 x D1 = W2 x D2 Use moments worksheet in resources folder

Using the principle of moments LO: Understand how things balance Using the principle of moments A student has an object of unknown mass, a model see-saw and a 0.5kg mass. How could he use the apparatus to find out the mass of the object? Place the 0.5kg mass and the object on the see-saw until they balance Work out the moments due to the 0.5kg mass This must be the same as the moments due to the object Divide by the distance of the object from the pivot to find the mass of the object Use moments worksheet in resources folder

LO: Understand how things balance Example 1 A student has an object of unknown mass, a model see-saw and a 0.5kg mass. When the 0.5kg mass is placed on the see-saw 0.3m from the pivot it balances with the object, which has been placed 0.5m from the pivot. What is the weight of the object? Use moments worksheet in resources folder

LO: Understand how things balance Example 2 A student has an object of unknown mass, a model see-saw and a 0.5kg mass. When the 1kg mass is placed on the see-saw 0.2m from the pivot it balances with the object, which has been placed 0.7m from the pivot. What is the weight of the object? Use moments worksheet in resources folder

Moment = force x distance from pivot LO: Understand how things balance Calculating moments Task: Answer the questions on calculating moments on the worksheet. The second side is more difficult than the first! Moment = force x distance from pivot Use moments worksheet in resources folder

What key words should you include in the explanation? LO: understand how to design stable objects Task Create a flow diagram to what happens to an object as it is gradually tilted until it falls over. Illustrate each stage with a picture. What key words should you include in the explanation?

Designing stable objects LO: understand how to design stable objects Designing stable objects Farmers must be careful when driving tractors on slopes. If the slope is too steep, the tractor may topple over. To limit the chances of this happening, tractors usually have a large base

Designing stable objects LO: understand how to design stable objects Designing stable objects This bus is being tested to find the maximum angle it can be tilted to before it topples over. This is important for road safety as it will affect the maximum speed that a driver can go around a corner.

LO: understand how to design stable objects High chairs A high chair has a centre of mass that is very high off the ground. This can make the chair very unstable, particularly when there is a baby strapped in! To make sure the chair does not topple over, it is designed to have a wide base.

LO: understand how to design stable objects Summary questions Make a list of objects that are designed to be difficult to knock over Think of an object that needs to be redesigned because it is knocked over too easily. Sketch the object and a possible redesign for it. A well designed baby chair has a wide base and a low seat. Explain why the chair would be unsafe if it had a narrow base and a high seat (use a diagram if it helps!) Explain why a tall plastic bottle is less stable when it is empty than when half full with water using the idea of moments and centre of mass.

Understand the motion of a pendulum KEYWORDS: oscillating, pendulum, The Pendulum Understand the motion of a pendulum ALL – Define the motion of a pendulum MOST – Explain how the time period of a pendulum can be increased SOME – Perform calculations involving time period and frequency KEYWORDS: oscillating, pendulum, Frequency, time period

LO: understand the motion of a pendulum The pendulum The picture shows a snapshot of a pendulum in motion. The pendulum moves backwards and forwards and always returns back to the middle, called the equilibrium position. This type of motion is called oscillating motion.

LO: understand the motion of a pendulum Time period The time period of a pendulum is the time it takes for a pendulum to complete one full cycle of motion. The easiest way to measure this is the time it takes for the pendulum to swing from one side of the pendulum to the other side and back again.

What affects the time period? LO: understand the motion of a pendulum What affects the time period? The factors that affect the time period of a pendulum are: The length of the pendulum The amplitude (maximum displacement) of the swing

Calculating time period LO: understand the motion of a pendulum Calculating time period The time period of a pendulum can be calculated using the following formula: T = 1 / f T = Time (s) f = frequency (Hz)

LO: understand the motion of a pendulum Example 1 A pendulum has a frequency of 50Hz. What is the time period for one oscillation?

LO: understand the motion of a pendulum Example 2 A pendulum has a time period of 0.5s. What is the frequency of oscillation of the pendulum?

LO: understand the motion of a pendulum Task A pendulum has a time period of 3s. What is the frequency of oscillation of the pendulum? A pendulum has a frequency of 100Hz. What is the time period of oscillation? A pendulum has a frequency of 20Hz. What is the time period of oscillation? A pendulum has a time period of 4s. What does the time period need to increase by so that the frequency of oscillation of the pendulum is 0.1Hz? A pendulum has a frequency of 0.2Hz. What does the time period need to reduce by for the pendulum to have a frequency of 0.25Hz?