Mechanics I

Displacement (definition)

The displacement of a particle from a fixed point is its distance from that point in a particular direction

Symbol + unit for displacement

[s], unit is metres (m)

Velocity (definition)

The rate of change of displacement w.r.t time

w.r.t meaning

With respect to

Velocity symbols + unit

Initial velocity [u], final velocity [v], unit is m/s or ms-1

Acceleration (definition)

The rate of change in velocity w.r.t time

Acceleration symbol + unit

[a] m/s squared or ms^-2

Scalar (definition)

A scalar is a quantity which has a magnitude only. E.g. time

Quantity (definition)

Something you can measure

Vector (definition)

A vector is a quantity which has a magnitude and a direction. E.g. displacement, velocity, acceleration, momentum, force

Scalars and their Vector Equivalent

Distance-Displacement, Speed-Velocity

Mass/Inertia definition

The measure of an object's ability to resist changes in its velocity

1st Equation of Motion

v=u+at

2nd Equation of Motion

s=ut+1/2at²

3rd Equation of Motion

v²=u²+ 2as

what does v mean?

final velocity

what does u mean?

initial velocity

what does t mean?

time

what does s mean?

distance

what does a mean?

acceleration

Equation for momentum

p=mv

What is the symbol for momentum?

p

What is the unit for momentum?

kgms^-1

The principle of conservation of momentum

States that in any closed system the total momentum before an interaction is equal to the total momentum after an interaction

Equation for an elastic collision

(m1)(u1)+(m2)(u2)=(m1)(v1)+(m2)(v2)

Equation for an inelastic collision

(m1)(u1)+(m2)(u2)=(m1+m2)v

What is an elastic collision?

objects bounce off one another. e.g. emerges

What is an inelastic collision?

Objects join each other. e.g. embedded

What is a closed system?

One in which there is no interaction between objects inside the system and objects outside the system. For example, a tennis player hitting a ball with a tennis raquet is not a closed system because the player can add or subtract momentum to the collision. If the tennis player threw the raquet at the ball it would be a closed system and the principle of conservation of momentum would apply

Draw how the principle of conservation of momentum applied to rockets diagram

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Draw how the principle of conservation of momentum applied to guns diagram

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Newton's First Law of Motion

A force is something which causes an object to change its velocity. The velocity of an object does not change unless a resultant force acts on it. This law defines what a force is. Force is measured in Newtons

Force (definition)

A force is something which causes an object to change its velocity.

Newton's Second Law of Motion

When a resultant external force acts on an object, the rate of change of the object’s momentum is directly proportional to the force, and takes place in the same direction. This law tells you what size the force is.

Equation for Newton's Second Law of Motion

F=ma

Addition and Resolution of Vectors (Co-Linear and in the same direction)

Add them, stays in the same direction

What is the resultant force?

The total force acting on an object

Addition and Resolution of Vectors (Co-Linear and in the opposite directions)

Subtract them, direction of the bigger force

Addition and Resolution of Vectors (Perpendicular to each other and tail to tail)

complete the parallelogram, find the magnitude using Pythagoras' Theorem, use SOHCAHTOA for the direction which is in degrees

Addition and Resolution of Vectors (Perpendicular to each other and head to tail)

complete the triangle, find the magnitude using Pythagoras' Theorem, use SOHCAHTOA for the direction in degrees

Resolution of a Vector

find the horizonal and vertical components. Use SOHCAHTOA

Resolution of a Vector (meaning)

Means splitting one vector into its horizontal and vertical components

Note on the "F=ma" equation

The F is always the resultant force

Newton's Third Law of Motion

In any interaction between two objects, a and b, the force exerted by a on b is equal in magnitude but opposite in direction to the force exerted by b on a. This tells us that forces occur in pairs

Newton's Third Law of Motion is more commonly known as

Every action has an equal but opposite reaction

Friction (definition)

The force which opposes motion between two objects in contact

Disadvantages of friction

Causes wear and tear, wastes fuel

Advantages of Friction

makes movement possible

Reduction of Friction

using a lubricant e.g. oil, grease. By streamlining. Using ball bearings