General Points
The gradient at any point is equal to the rate of change of acceleration, not a very meaningful quantity. In particular a horizontal line has zero acceleration or constant velocity.
At any time when the graph intercepts the t axis, the acceleration AT THAT INSTANT is zero.
The area under an acceleration time graph is equal to the velocity. For the example above, the velocity after 7 s is
If the acceleration is constant the graph of acceleration against time is a horizontal line with the y – value equal to the acceleration. The acceleration illustrated in the graph below is
Given any body, the position of the centre of gravity can be found by hanging it from several different points. When it is hanging from any point, the position of the centre of gravity will be below the balance point. Draw a line from this point vertically down. Do this for several hanging points (P,Q and R in the diagram below) and the intersection of these lines will be the centre of gravity (C.G.).
It is important to realise the centre of gravity does not have to be within the object. The centre of gravity of a boomerang is outside the boomerang, as shown below.
]]>If the force pushing the block increases, so does the frictional force, but only up to a limit. The maximum frictional force is proportional to the normal reaction force, labelled N in the diagram above. The constant of proportionality is called the coefficient of static friction and labelledThe s indicates that it is for static friction. We can write
If the maximum frictional force is reached, the block is said to be in a state of limiting equilibrium.
It should be noted that
The coefficient of friction defined above is for static friction, such that the block does not move. If the block is in motion, then we use the coefficient of dynamic frictionand writeDynamic friction is always less than static friction, so
The coefficient of friction – whichever definition is used – is a ratio of forces and is dimensionless. It has no units.
The coefficient of friction between smooth surfaces is zero.
The coefficient of friction is less than one unless the surfaces are stuck together.
The frictional force acts along the interface between the two bodies in contact.
The frictional force always opposes motion. If the tendency to move changes direction, so does the frictional force, still opposing motion.
The only force acting on a projectile is the force of gravity. Air resistance is ignored. Gravity is a vertical force, acting downwards,. There are no horizontal forces therefore, and no horizontal acceleration. The horizontal velocity, vfrom the diagram below.
The projectile accelerates downwards with an acceleration g. We can use the equation of motionvertically to obtain the vertical component of the velocity at any timeWithwe haveThis means that v decreases as t increases, becoming zero at the highest point and negative thereafter.
]]>Some common definitions used in kinematics are given in the table below, with some of their properties.
Quantity 
Symbol 
Definition 
Example 
SI Unit 
Vector or Scalar 
Displacement 
Distance moved in a particular direction 
The displacement from London to Birmingham is 120 miles North West 
Metre (m) 
Vector 

Velocity 
or 
Rate of change of displacement 
The average velocity of a 2 hour car journey from London to Birmingham is 60 mph North West 
Metres per second (m/s) 
Vector 
Speed 
V or u 
Rate of change of distance 
The average rate speed of a two hour journey from London to Birmingham is 65 mph. Notice this is higher than the velocity. The distance travelled is at least equal to the displacement. 
Metres per second (m/s) 
Scalar 
Acceleration 
Rate of change of velocity 
for motion in a circle radius 
m/s/s 
Vector 

Momentum 
Product of mass and velocity 
A particle mass 1 kg moving in the x direction with speed 3 m/s has momentum 3 kg m/s 
Kg m/s 
Vector 

force 
Rate of change of momentum, also expressed as 
If the particle above accelerates from 0 to 3 m/s in 2 s then the momentum has changed from 0 to 3 kg m/s in 2 s so the force isin the direction of acceleration 
newton (N) 
vector 

Impulse 
Change in momentum, often during collisions or when a body experiences a force 
The body above receives an impulse of 3 kg m/s 
kg m/s 
Vector

Name of force  Description 
Gravitational  The force between objects of massand separated by a distanceas a result of their masses, also called the weight in the gravitational field of the other. Given by the equation the – indicates an attractive force, in the direction of r decreasing. 
Electrostatic force  The force between objects separated by a distance r as a result of their electric charges andgiven byThe force is repulsive, in direction of increasingforof like sign and attractive for unlike charges. 
Magnetic force  The force between magnets/currents 
Normal reaction  The force between surfaces in contact. The normal reaction force is always at rightangles to the point of contact. If the surfaces are smooth, it is the only force between them. 
Friction  The forces that oppose the sliding of surfaces in contact past each other. Acts along the surfaces. Air resistance can be thought of as friction. 
Tension  When a string is stretched, a tension is produced in the string, always acting towards the centre of the string. When the string is attached to an object it will exert a force on the object equal to the tension. 
Compression  When a rod is compressed, it experiences a force pushing the ends of the rod inwards. A force is produced opposing further compression. If the ends of the rod are put in contact with another object, they exert a force equal to the compressive force. 
Upthrust  The force that acts on an object submerged in a fluid. It is equal to the weight of fluid displaced by Archimedes principle and acts upwards. 
Lift  The force produced on an object when a fluid flows over it in an asymmetrical way. The shape of an aircraft wing causes lift which enables the aircraft to fly. 
General Points
The gradient at any point is equal to the rate of change of displacement, or the velocity. In particular a horizontal line has zero velocity or constant displacement.
At any time when the graph intercepts the t axis, the displacement AT THAT INSTANT is zero.
The area under an displacement time graph has no real meaning.
If the displacement is constant the graph of displacement against time is a horizontal line with the y – value equal to the displacement. The displacement illustrated in the graph below is 15 m.
We can write
Once the object starts to move friction reduces slightly as shown below.
The coefficient of friction depends on the two surfaces. Some are given below.
Surfaces 
µ (static) 
µ (kinetic) 
Steel on steel 
0.74 
0.57 
Glass on glass 
0.94 
0.4 
Metal on Metal (lubricated) 
0.15 
0.06 
Ice on ice 
0.1 
0.03 
Teflon on Teflon 
0.04 
0.04 
Tire on concrete 
1 
0.8 
Tire on wet road 
0.6 
0.4 
Tire on snow 
0.3 
0.2 
Examples: There is friction in the bearings of engines and wheels. The friction can be reduced with the use of lubricating oil but it cannot be eliminated.
]]>The efficiency of a machine or process is defined as one of:
Many machines are surprisingly inefficient. Only about 15% of the chemical energy of the fuel for a car is transferred into actual kinetic energy of the car on average. A typical power station is only about 30% efficient. The muscles in the human body are of the same order of efficiency – maybe 18 to 26%.
The useful power can depend on the context. Some machines are designed to be 0% inefficient in the sense that the useful mechanical energy produced is zereo. For example, brakes are DESIGNED to turn kinetic energy into heat energy. The efficiency of brakes according to any definition above is zero, since all the kinetic energy of the vehicle is changed into heat energy which cannot be recovered to do mechanical work but this does not mean the effectiveness of the brakes is low or can be improved. A heating element is designed to turn electrical energy into heat energy, which in many electrical devices would be considered a form of waste energy.
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