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