opic: 1.1 Physical Quantities and Measurement Techniques
#### 1. Scalars and Vectors
| Scalar Quantities (Magnitude only) | Vector Quantities (Magnitude and Direction) |
| :--------------------------------------------------------------------------------------------------------------------------------- | :-------------------------------------------------------------------------------------------------------------------------------------------- |
| - Distance: Total length travelled (e.g., 5 m) | - Force: A push or a pull (e.g., 20 N downwards) |
| - Speed: Distance travelled per unit time (e.g., 10 m/s) | - Weight: The force of gravity on a mass (e.g., 50 N towards the centre of the Earth) |
| - Time: Duration of an event (e.g., 12 s) | - Velocity: Speed in a given direction (e.g., 5 m/s East) |
| - Mass: Amount of matter in an object (e.g., 15 kg) | - Acceleration: Change in velocity per unit time (e.g., 9.8 m/sĀ² downwards) |
| - Energy: The capacity to do work (e.g., 100 J) | - Momentum: Mass Ć velocity (e.g., 30 kg m/s to the right) |
| - Temperature: Degree of hotness (e.g., 20 Ā°C) | - Field Strength (Electric/Gravitational): Force per unit charge/mass (e.g., 10 N/C left) |
Key Point: Vectors can be represented by arrows. The length shows the magnitude, and the direction of the arrow shows the direction.
#### 2. Finding the Resultant of Two Vectors at Right Angles
For two perpendicular vectors (e.g., a force of 3N North and a force of 4N East):
* By Calculation:
* Magnitude: Use Pythagoras' theorem.
* Resultant Force, $R = \sqrt{3^2 + 4^2} = \sqrt{9 + 16} = \sqrt{25} = 5$ N
* Direction: Use trigonometry (tanĪø = opposite/adjacent).
* Īø = tanā»Ā¹(4/3) ā 53.1Ā° from North towards East (or E 53.1Ā° N).
* Graphically:
1. Choose a scale (e.g., 1 cm = 1 N).
2. Draw the first vector as an arrow of correct length and direction.
3. From the tip of the first arrow, draw the second vector to scale.
4. The resultant vector is the arrow drawn from the tail of the first vector to the tip of the last vector.
5. Measure its length and convert back using the scale to find the magnitude. Measure the angle with a protractor to find the direction.
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### Measurement Techniques
#### 1. Measuring Length and Volume
* Ruler: Used to measure lengths between 1 mm and 1 m.
* Precaution: Avoid parallax error by looking perpendicularly at the scale.
* Micrometer Screw Gauge: Used for very small distances (e.g., paper thickness, wire diameter).
* How to use:
1. Check and set the zero error before use.
2. Place the object between the anvil and the spindle.
3. Turn the ratchet until it slips (do not overtighten).
4. Take the reading from the main scale (mm) and the circular scale (0.01mm).
* Finding paper thickness:
1. Measure the thickness of a large stack (e.g., 100 sheets).
2. Divide the total reading by the number of sheets to find the average thickness of one sheet.
* Measuring Cylinder: Used to find volume.
* For a liquid: Read the volume directly from the meniscus at eye level.
* For an irregular solid:
1. Fill the cylinder with water and note the volume ($V_1$).
2. Lower the object into the water (ensure it is fully submerged).
3. Note the new water level ($V_2$).
4. Volume of object = $V_2 - V_1$ (displacement method).
#### 2. Measuring Time Intervals
* Clocks & Digital Timers: Used to measure time intervals.
* Measuring Short Time Intervals: To improve accuracy, measure the time for multiple events and find the average.
This reduces the *percentage uncertainty** associated with human reaction time.
Specific Examples:
* Period of a Pendulum / Piston Cycle:
1. Time a large number of complete oscillations/cycles (e.g., 20 oscillations).
2. Divide the total time by the number of oscillations to find the average period.
3. Precautions:
Start and stop the stopwatch at a *fixed (fiducial) point** in the cycle (e.g., at the bottom of the swing for a pendulum).
* Repeat the timing and calculate a mean average.
* Check for zero error on the stopwatch.
* Analysing a set of readings (e.g., 1.8s, 1.9s, 1.7s...):
The *best value** is the mean (average) of all the readings.
Calculation: (1.8+1.9+1.7+1.9+1.8+1.8+1.9+1.7+1.8+1.8) / 10 = *1.81 s**
#### 3. Measuring Amplitude
* For a pendulum:
1. Measure the horizontal distance from the equilibrium (rest) position to the maximum displacement point using a ruler.
2. Alternatively, measure the angle from the vertical to the string at its maximum displacement using a protractor.
* Precaution: Avoid parallax error by ensuring your eye is level with the measurement.
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### Definitions and Key Concepts
#### 1. Acceleration
* Definition: Acceleration is the rate of change of velocity.
* Equation: $a = \frac{(v - u)}{t}$ OR $a = \frac{\Delta v}{t}$
* Where:
* $a$ = acceleration (m/sĀ²)
* $v$ = final velocity (m/s)
* $u$ = initial velocity (m/s)
* $t$ = time taken (s)
* $\Delta v$ = change in velocity (m/s)
#### 2. Interpreting Motion (Forces and Acceleration)
* (a) Acceleration and Speed:
* Positive acceleration means speed is increasing.
* Zero acceleration means constant speed (terminal velocity).
* Negative acceleration (deceleration) means speed is decreasing.
* (b) Forces and Acceleration:
A *resultant force** causes acceleration ($F = m \times a$).
If the acceleration is *zero**, the resultant force is zero (e.g., driving force equals friction, or weight equals air resistance).
* Why acceleration decreases to zero during a skier's descent:
As speed increases, *air resistance/friction** increases.
* Eventually, air resistance becomes equal in magnitude but opposite in direction to the component of the weight driving the skier down the slope.
The *resultant force becomes zero**, and so acceleration becomes zero. The skier continues at a constant terminal velocity.