Forces class 1 (newtons first and second law)

Essential Context and Goals

This lecture contrasts IGCSE and IB DP approaches to Newton's laws: IB DP expects you to follow Newton's laws even when instincts clash with them.
The focus will be on applying laws to everyday and exam-style questions, not just memorizing laws.
You will see questions where the correct answer follows Newton's laws rather than instinctive intuition; practice both “with” and “against” instinct to strengthen understanding.
A sequence of IT questions (short quiz) will be used to rehearse applying the laws to familiar scenarios before moving to more challenging concepts.
Slides will be shared regularly; focus on major revelations or epiphanies that clarify problem solving, not every detail.

Essential vocabulary and core concepts

Normal reaction force (N): the solid-surface pushback that prevents penetration; acts perpendicular to the contact surface. Example: ground pushes up on you when you stand or rest on a table.
Weight (W): the gravitational force pulling an object toward the center of the Earth.
Friction: a contact force opposing motion or impending motion, acting parallel to surfaces in contact.
Net force (F_net): the vector sum of all forces acting on an object; determines acceleration.
Translational equilibrium: a state where the net force is zero, so there is no acceleration; velocity is constant (including zero for a stationary object). Also called Newton's first law in a form focused on translation.
Newton's first law (translational): If there is no net force, the velocity is constant; equivalently, if there is a net force, there is acceleration.
Newton's second law (F = ma): the net force acting on an object equals the mass times its acceleration, assuming constant mass during the motion being analyzed.
Mass (m): a measure of an object's resistance to acceleration; assumed constant in the standard F = ma form.
Acceleration (a): rate of change of velocity; the vector quantity describing how velocity changes with time.
Velocity (v) vs Speed (s): velocity is the rate of change of displacement (vector), speed is the rate of change of distance (scalar). 95% of the time they coincide; they differ when direction (displacement) matters or when a question specifically tests the difference between them.
Displacement (Δs): straight-line difference between an object's initial and final position; depends on the reference point and direction.
Distance: total length of the path traveled; independent of direction.
Position (r or (x, y, z)): location of an object in a chosen coordinate system; can be used to compute velocity via differentiation.
Vector vs scalar language: keep track of directions; F_net and a are vectors in general, but the common classroom examples often use one dimension where they are scalars.

Distinguishing key quantities: velocity, speed, displacement, distance, and position

Velocity is the rate of change of displacement: oldsymbol{v} = rac{doldsymbol{s}}{dt}
Speed is the rate of change of distance: v = rac{ds}{dt}
Displacement is the straight-line change in position from start to finish: the length and direction of the red line in a path diagram; not necessarily equal to path length.
Position is the coordinates of the object at a given time; e.g., in 3D, oldsymbol{r} = (x, y, z), and the distance from the origin is |oldsymbol{r}| =
sqrt{x^2 + y^2 + z^2}
Acceleration is the rate of change of velocity: oldsymbol{a} = rac{doldsymbol{v}}{dt}
In linear motion (one dimension), these reduce to scalar forms with signs indicating directions.

How forces relate to motion: Newton's laws in practice

Forces do not directly set speed; they determine acceleration via: oxed{F_{net} = m a}
The net force is the single resultant force that would produce the same motion as all the individual forces combined. For a given problem, identify the net/unbalanced force first.
Mass is assumed constant when using F = ma; changes in mass require a more general treatment.
The direction of the net force determines the direction of the acceleration, not necessarily the instantaneous direction of motion.
When the net force is zero, the acceleration is zero and the object moves with constant velocity (could be zero velocity). This is translational equilibrium.
The force you apply (e.g., pushing a trolley) and the friction or other resistive forces together determine the net force and hence the acceleration.

Translational equilibrium and practical implications

Translational equilibrium is another phrase for Newton's first law in the context of linear motion:
- If the net force on an object is zero, its velocity is constant.
- An object at rest stays at rest; an object in uniform straight-line motion continues in that motion.
Rotational equilibrium is not on the current Excel syllabus; focus remains on translational forces and motion for now.

Worked examples and practical demonstrations discussed

Example 1: A trolley on a table with friction
- Given: mass m = 5000 kg; an applied force results in acceleration a = 0.4 m/s^2.
- Compute net force: F_{net} = m a = 5000 imes 0.4 = 2000 ext{ N}
- If the applied driving force is 6000 N and friction opposes motion, then frictional force is:
- Friction F_fric = 6000 N - 2000 N = 4000 N
- Interpretation: Net force is the resultant of all forces; only 2000 N is accelerating the trolley; part of the applied force is balanced by friction.
Example 2: Space-like thought experiment (no external forces after release)
- If an object is thrown in space with no forces acting on it (no gravity, no friction, no drag), it will continue in a straight line at constant velocity indefinitely, per translational equilibrium once the net force is zero.
- If you imagine a region far from gravitational influence, the object would not slow down or change direction due to forces in that region.
- The discussion includes a caveat about space expansion; in classical mechanics, such cosmological effects are not typically modeled alongside simple F = ma problems.
Example 3: Bird path vs displacement vs distance
- If a bird flies along a curved path and ends up at a point, its distance traveled is the total length of the path; its displacement is the straight-line distance from start to finish.
- Velocity is the rate of change of displacement; speed is the rate of change of distance.
- This distinction helps distinguish what is being asked in a problem: if a question tests velocity, use displacement; if it tests speed, use distance.
Example 4: Translation of a velocity-time scenario into acceleration
- Given a table of velocity at different times, acceleration can be found from the slope: a = rac{v2 - v1}{t2 - t1}
- In the discussed scenario, a constant acceleration of a = 5 ext{ m s}^{-2} was derived from velocity changes over time: for instance, from 2 s to 4 s the velocity changes by 10 m/s (2→12 m/s over 2 s), giving a = rac{12 - 2}{2} = 5 ext{ m s}^{-2}
- They emphasize that the acceleration is the key quantity that drives motion, not the absolute numbers in the table alone.

Practical problem-solving approach (F = ma focused)

Step 1: Identify the net force acting on the object. List all forces: weight, normal reaction, friction, applied forces, etc.
Step 2: Check if the net force is zero or not. If zero, acceleration is zero and the motion is constant (translational equilibrium).
Step 3: If not zero, use: F_{net} = m a to find the acceleration. Remember to use the net force (the sum of all forces with proper directions).
Step 4: Use the appropriate data to compute the acceleration, then infer velocity or position as needed.
Step 5: Be careful with symbols: ensure what each F represents in a problem is indeed the net force; confusing different problems’ force symbols is a common source of error.
Step 6: For questions about direction of motion, use clues from the problem (e.g., staged forces) to determine possible acceleration direction; if direction of motion is not fully determined, describe the acceleration direction based on net force.
Step 7: Remember the difference between instantaneous rates (velocity, acceleration) and cumulative quantities (position, displacement, distance).

Notation, units, and conventions (iBTP standardization)

Acceleration is typically written and read as a = rac{d v}{d t} in symbols; in one-dimension, the scalar form is used with sign to indicate direction.
Common classroom notation: a = rac{v2 - v1}{t2 - t1} for average acceleration over a time interval.
Common units: a ext{ in } ext{m s}^{-2}, ext{ } F ext{ in N (Newtons)}, ext{ } m ext{ in kg} when using SI units.
In iBTP style, the acceleration unit is often written as ext{m s}^{-2} rather than the old style ext{m s}^{-2} (with the hyphenless variant historically used in different curricula).

Quick recap of the core relationships

If a net force acts on a mass, the object accelerates: F_{net} = m a
If no net force acts, the velocity is constant (could be zero): translational equilibrium.
Acceleration changes velocity; velocity changes displacement, and hence the distinction between speed and velocity matters depending on the question.
The normal reaction force is an upforce from a surface; it balances weight in many static or quasi-static situations, contributing to a net-force balance in the vertical direction.

What to take away for exams and future study

Expect questions where Newton's laws contradict everyday intuition; rely on the law rather than instinct.
Begin problems by determining net force, then apply F = ma to get acceleration; from there determine velocity or position as required.
Distinguish between displacement vs distance (and velocity vs speed) clearly; know which quantity a question is testing.
Be prepared for trivial-looking problems on relatively advanced topics (e.g., special relativity) that are framed to be as approachable as possible; the challenge often lies in the conceptual leap rather than the calculation.
Slides will be circulated; focus your notes on major revelations that clarify how to solve common problem types, not every line of the lecture.

Quick practice prompts (from the lecture prompts mentioned)

When given a diagram or table of forces, identify the net force and determine whether the motion is constant or accelerating.
For a trolley with several forces, compute the net force first, then the acceleration, and finally the frictional forces if they are the balancing forces.
Determine whether an object in hypothetical space would continue at a constant velocity or slow down, given the presence or absence of net external forces.
Distinguish between the different definitions (velocity, speed, displacement, distance) by reading a problem carefully to identify what is being asked."