Physics Measurements and Motion

Measurements in Physics

Fundamental Units:
- Length: Meter (m)
- Mass: Kilogram (kg)
- Time: Second (s)
Derived Units:
- Velocity: Meters per second (m/s)
- Acceleration: Meters per second squared (m/s²)
- Force: Newton (N), where 1 N = 1 kg·m/s²
Measurement Tools:
- Ruler: For measuring lengths.
- Balance: For measuring mass.
- Stopwatch: For measuring time intervals.
Accuracy vs. Precision:
- Accuracy: How close a measurement is to the true value.
- Precision: How consistent repeated measurements are.
Significant Figures:
- Indicate the precision of a measurement.
- Rules for determining significant figures include:
  - Non-zero digits are always significant.
  - Any zeros between significant digits are significant.
  - Leading zeros are not significant.
  - Trailing zeros in a decimal number are significant.

Motion

Types of Motion:
- Linear Motion: Movement in a straight line.
- Rotational Motion: Movement around a central point or axis.
- Oscillatory Motion: Repetitive back and forth movement.
Describing Motion:
- Displacement: Change in position; vector quantity.
- Distance: Total path length; scalar quantity.
- Speed: Distance traveled per unit time; scalar quantity.
- Velocity: Displacement per unit time; vector quantity.
Acceleration:
- Change in velocity over time; can be positive (increasing speed) or negative (deceleration).
- Formula: ( a = \frac{\Delta v}{\Delta t} )
Newton's Laws of Motion:
- First Law (Inertia): An object at rest stays at rest, and an object in motion stays in motion unless acted upon by a net force.
- Second Law: ( F = ma ) (Force equals mass times acceleration).
- Third Law: For every action, there is an equal and opposite reaction.
Graphs of Motion:
- Position vs. Time: Slope represents velocity.
- Velocity vs. Time: Slope represents acceleration; area under the curve represents displacement.
Kinematics Equations (for uniformly accelerated motion):
- ( v = u + at )
- ( s = ut + \frac{1}{2}at^2 )
- ( v^2 = u^2 + 2as )
- where:
  - ( s ) = displacement
  - ( u ) = initial velocity
  - ( v ) = final velocity
  - ( a ) = acceleration
  - ( t ) = time

Measurements in Physics

Fundamental units are the basic building blocks of measurement:
- Length (meter), Mass (kilogram), Time (second).
Derived units are formulated from fundamental units:
- Velocity is expressed as meters per second (m/s).
- Acceleration is measured in meters per second squared (m/s²).
- Force is quantified in Newtons (N), where 1 N equals the product of mass (kg) and acceleration (m/s²).
Common measurement tools include:
- Rulers for measuring length.
- Balances for determining mass.
- Stopwatches for timing events.
Understanding accuracy and precision:
- Accuracy refers to how closely a measurement aligns with the true value.
- Precision indicates the consistency of repeated measurements.
Significant figures reflect the precision of measurements:
- Non-zero digits are always significant.
- Zeros between significant digits count as significant.
- Leading zeros do not count as significant figures.
- Trailing zeros in decimal numbers are significant.

Motion

Types of motion encompass:
- Linear motion: movement along a straight path.
- Rotational motion: circular movement around an axis.
- Oscillatory motion: motion that moves back and forth over time.
Key descriptors of motion include:
- Displacement is the vector metric indicating the change in position.
- Distance measures the total length of the path traveled, a scalar quantity.
- Speed is defined as the distance traveled per unit time, also a scalar quantity.
- Velocity represents displacement per unit time and is a vector quantity.
Acceleration characterizes the change in velocity over time, can be:
- Positive (increasing speed) or negative (deceleration).
- The acceleration formula is ( a = \frac{\Delta v}{\Delta t} ).
Newton's Laws of Motion provide fundamental principles:
- First Law (Inertia): An object remains in its state of motion unless influenced by a net force.
- Second Law: Can be expressed as ( F = ma ), highlighting the relationship between force, mass, and acceleration.
- Third Law: States that every action has an equal and opposite reaction.
Graphical representations of motion:
- Position vs. Time graph: The slope indicates the object's velocity.
- Velocity vs. Time graph: The slope reflects acceleration, while the area under the curve shows displacement.
Kinematics equations for uniformly accelerated motion include:
- ( v = u + at ) relates final velocity to initial velocity, acceleration, and time.
- ( s = ut + \frac{1}{2}at^2 ) computes displacement considering initial velocity and acceleration.
- ( v^2 = u^2 + 2as ) connects final velocity, initial velocity, acceleration, and displacement.
- Variables include:
  - ( s ): displacement
  - ( u ): initial velocity
  - ( v ): final velocity
  - ( a ): acceleration
  - ( t ): time