SI Units
- There are 7 basic quantities and units:
- Electrical Current – Amperes (A)
- Luminous Intensity – Candela (cd)
- Temperature-Kelvin.(K)
- Mass – Kilogram ( Kg)
- Length – Metre (m)
- Amount -Mole (mol)
- Time -Second (s)
Prefixes used for scalar & vector quantities:
- kilo: $10^{3}(\mathrm{k})$
- Deci: $10^{-1}(d)$
- Centi: $10^{-2}(\mathrm{c})$
- Milli: $\left.10^{-3} \mathrm{~m}\right)$
- Micro:$10^{-6} (\mathrm{N})$
- Nano:$10^{-9} (\mathrm{n})$
FORCES & ENERGY
- Force
- This defines as simply an agent that produces or tends to produce motion and/or rest.
- Speed
- This defines as the distance moved by an object in a given period of time. The formula for speed is:
$
\text { average speed }=\frac{\text { distance moved }}{\text { time taken }}
$
- Speed can be measured in units such as meters per second (m/s), kilometers per hour (km/hr), or miles per hour (mi/hr).
- Speed is a scalar quantity (has only magnitude).
- Velocity is speed in a certain direction, making it a vector quantity. The formula for velocity is:
$
\text { velocity }=\frac{\text { displacement }}{\text { time }}
$
- Velocity is a vector quantity has both magnitude and direction. This described how fast and in what direction an object is moving.
- Velocity can be expressed the same units as speed (m/s, km/hr, or mi/hr).
- Meanwhile, acceleration is the measure of the rate of increase in velocity. This is also described as a vector quantity. The formula for acceleration is:
$
\text { acceleration }=\frac{\text { increase in velocity }}{\text { time taken }}
$
- It measures how quickly the object speeds up, or slows down, or changes its direction.
- Acceleration can be expressed in a unit, meters per second square (m/s2).
Concept of Acceleration
- Positive Acceleration
- When an object’s velocity increases over time, it has a positive acceleration. For example: A car speeding up as it moves forward.
- Negative Acceleration or Deceleration, or Retardation
- When an object’s velocity decreases over time, it decelerates. For example: A car slowing down to stop.
- If an object decelerates at $3 \mathrm{~m} / \mathrm{s}^{2}$, its acceleration is $-3 \mathrm{~m} / \mathrm{s}^{2}$.
- Although $\mathrm{m} / \mathrm{s}^2$ is acceptable, the unit $\mathrm{ms}^{-1}$ is more commonly accepted.
$
\frac{m}{s^2}=m s^{-1}
Importance of Acceleration
- Acceleration helps describe how forces act on objects, as shown in the Newton’s Laws of Motion (F= ma).
- It is essential in understanding motion of objects such as circular motion, projectile motion, and dynamics of moving bodies.
Graphical Presentation of Motion
1.A distance-time graph is plotted to show the increase in distance over time. Further, this explains that this graph plots the distance on the y-axis (vertical) and the time on the x-axis (horizontal), and this shows how far the objects travel in a particular time.
- The straight upward sloping line indicates a constant speed. A horizontal line indicates that the object is stationary. A curved line- steepening or flattening indicates acceleration or deceleration.
- The gradient of the distance – time graph shows the velocity of the car. this can be found using:
Gradient $=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}$ – Distance Time graph for $E$ an accelerating car.
Example: A rider rides at a constant speed of 5 meters per second (m/s) for 10 seconds (s). Then, the graph will show a straight upward line from, (0,0) to (10, 50), and if the rider stops for 5 seconds then the graph becomes horizontal during that period.
2. A velocity-time graph shows the changing velocity over time. Further explains that this graph plots velocity on the y-axis (vertical) and time on the x-axis (horizontal) which basically shows how velocity changes over time.
- The gradient of a velocity-time graph is the acceleration of that specific object (same formula).
- The area under a velocity-time graph is the distance that object has moved.
There are 3 main equations of motion. These are:
(1) $v=u+a t$
(2) $S=u t+\frac{1}{2} a t^{2}$
(3) $v^{2}=v^{2}+2 a s$
where
$v=$ final velocity
$U=$ initial velocity
$s=$ distance
$t=$ time
$a=$ acceleration FO: FUT
- While they may be used interchangoly, Mass and Weight are completely different things. The differences are:
- The gravitational strength of Earth is almost constant $\rightarrow 9.8 \mathrm{~m} / \mathrm{s}^2$ or $\mathrm{ms}^{21}$. However, it should be noted that in the cases of free fall, a (acceleration $)=g$.
Common Example
A person on a building drops a ball (not throwing with force) FUCHS
- However, it should be noted that an object only accelerates until it reaches its terminal velocity. Teminal velocity is the highest attainable velocity of an object while falling through mid-air.
It can be fond using.
$
v=\sqrt{\frac{2 m g}{p A C}} \text {, where }
$
$v=\sqrt{\frac{2 m g}{p A C}}$, where
$v=$ terminal velocity
$m=$ mass of falling abject
$g=$ gravitational acceleration
$p=$ density of fluid through which the object is falling
$A=$ the projected area of the object
$C=$ the drag coefficient
- The value of $g$ varies slightly from place to place on Earth, but is roughly $\approx 9.8 \mathrm{~ms}^{-1}$. Date
- Gravity pulls all objects towards the earth at the same time naturally. However, some light objects fall slowerdoe to air resistance. This is why all objects would fall together in a vacuum.
- Force, mass and acceleration are all relatable. Isaac Newton’s 3 laws of motion best describes them.
Newton’s Laws of motion:
1) Every object persists in its state of rest or uniform motion in a straight line unless it is compelled to change that state by forces impressed on it.
2) Force is equal to the change, in momentum per change in time. For. a constant mass, force equals mass times acceleration.
3) For every action, there is an equal and opposite reaction.
- The first law of motion explains how everything has inertia to change in state of motion or rest. It with remain stationary or moving unless external forces act upon it.
- The second law can be summarized:
Force $=$ mass $\times$ acceleration $(F=m a)$, or can be replaced by
- Weight = mass $x$ gravitational strength (w=mg)
- The third law of motion explains how the net result of every force is 0 , due to an equal but opposite reaction.
- How force/weight changes from Earth to moon $(f=w,g=a)$
Mass is constant, while weight changes
- When materials try to slide across each other, a force called friction stops them. The types of friction are:
- Static: The friction between objects that start to slide.
- Dynamic: The friction during the sliding
- Fluid: The friction caused when an object tries to slide inside a gas or a liquid.
- There are several types of motion:
- Straight-line motion
- Projectile motion
- Centripetal motion
- Centripetal motion is circular motion produced by forces applied at right-angles. This can be found by:
$
\begin{aligned}
& \text { Centripetal force }=\frac{m v^2}{r_{\text {radius of }}} \\
\\
&
\end{aligned}
$
- Immediately after centripetal force, if the wire or what is causing right-angular motion stops doing so, the object will travel straight on due to centrifugal force:
- The earth’s gravity also causes objects such as satellites to travel in centripetal motion. To escape this, the object must reach escape velocity, which is $11,000 \mathrm{~m} / \mathrm{s}$.
- The momentum of an object is its mass $x$ velocity. It is the “quantity” of motion in a moving body:
(1) Momentum $=$ mass $x$ velocity
(2) Force $=\frac{m v-m v}{t}$, where
mv is the final momentum
mu is the initial momentum
so
Force $=$ rate of change of momentum
- This formula can be rearranged to say:
$\begin{aligned}
& F t=m v-m v \\
& \text { Impulse } \\
& \text { Gain in momentum } \\
&
\end{aligned}$
- Impulse is really just the change in momentum.
- Momentum is conserved when two objects collide. Their sum remains the same:
- This can be given from the formula
$
\left(m_1 \times v_1\right)+\left(m_2 \times v_2\right)=m_1 v+m_2 v
$ - V is constant as the final velocity will remain the same:
- All this confirms Newton’s $2^{\text {nd }}$ Law.
- Finding resultant forces between objects directly horizontal or vertical) is simple addition/subtraction
- The resultant forces of angular forces is found by the Parallelogram we:
When two forces act at a point.
When two forces act at a point, their resultant is found by the law of parallelogram of forces.
The magnitude of Resultant force R
$
R=\sqrt{P^2+Q^2+2 P Q \cos } \alpha
$
The direction of Resultant force $\mathrm{R}$ with the force $\mathrm{P}$
$
\theta=\tan ^{-1}\left(\frac{Q \sin \alpha}{P+Q \cos \alpha}\right)
$
- Two forces can also be acting on the same object. If the object is straight, it is in a state of equilibrium, where the clockwise and anfi-clockwise moments are equal. A moment of a force is a measure of the turning effect of the force about a particular point. It is found by:
$\begin{aligned} & \text { Moment }=\text { force } \times \text { distance } \\ & (\mathrm{Nm}) \ (\mathrm{N}) \quad(m)\end{aligned}$
Example of Equilibrium:
- For equilibrium, the sum of forces in one direction must equal those of the other direction. Plus, the principe of moments must apply.
- Using, the principle/concept of moments, couples are created? These are long, parallel yet opposite forces.
- The moment amount of a couple is called its torque.
- Considering the rules for equilibrium, there ore different forras of stability. These are dependent upon:
- Center of gravity: Where the weight of an object pulls.
- Center of mass: The mean position of the mass of an -object.
- There are 3 types of equilibrium:
- Work (in Physics) is done when a fore produces movement. The SI unit for work is Joule. It can be found by:
- To work, everything needs energy. The re are different types of these:
- Thermal : Heat
- Kinetic: Moving
- Potential : stored
- Electrical: Relating to current
- Chemical: Relating to chemicals
- Kinetic energy is created when particles collide with one another, causing effective collision. This process can be sped up by providing more heat to the particles reducing their masses,kinetic energy can be determined using the formula:
Kinetic Energy $=\frac{1}{2} m v^2$
- Potential energy is the stored energy and is found by:
Potential Energy $=m g h$
- Energy cannot be created or destogel, it only converts into other forms. After the work is done, the energy is subsequently transferred
- The energy crisis has taken a step forward in the whole world, for which, new methods have to be come up with. But they are releasing carbon dioxide and causing Climate Change (see IDU topic).
The power of any energy source is the rate at which it gets work done. It can be measured by:
$
\text { Power }=\frac{\text { work done }}{\text { time }}=\frac{\text { energy transfered}}{\text { time }}
$
- It is measured by watts (w)
- In motion examples, it is true that:
$
\text { Power }=\text { force } \times \text { velocity }
$
- The efficiency of an energy source is hence also measured by:
$
\text { Efficiency }=\frac{\text { Power output }}{\text { power input }}
$