Regents Physics forces: a complete skills guide to Newton's three laws, weight, the normal force, friction, free-body diagrams and equilibrium

Why forces are the engine of Regents mechanics

Kinematics describes motion; forces explain it. Every acceleration in the course traces back to a net force through Newton's second law, and the recurring skill is to draw a free-body diagram, combine the forces, and reason from force to motion. This guide ties together the dot-point pages, each with its own practice: Newton's first law and inertia, Newton's second law, Newton's third law, weight and the normal force, friction and equilibrium and free-body diagrams.

Newton's three laws

The three laws form a single picture of how forces and motion relate:

• First law (inertia): an object stays at rest or moves at constant velocity unless a non-zero net force acts. Inertia (resistance to a change in motion) is measured by mass. Constant velocity or rest signals a zero net force.
• Second law: $F_{net} = ma$. Acceleration is proportional to the net force and inversely proportional to mass, in the direction of the net force. Find the net force first, then divide by the mass.
• Third law: forces occur in equal and opposite pairs acting on different objects, so a pair never cancels and never appears together on one free-body diagram.

The first law is the $a = 0$ case of the second; the third explains propulsion (push back on the ground, water or exhaust gas, and it pushes you forward) and underlies the conservation of momentum.

Weight, the normal force and friction

These are the specific forces that fill a free-body diagram:

• Weight: $F_g = mg$, always straight down, with $g = 9.81$ m/s squared. Mass (kilograms) is the amount of matter; weight (newtons) is the force.
• Normal force: $F_N$, perpendicular to a surface. On a level surface with no other vertical force, $F_N = mg$; on an incline, $F_N = mg\cos\theta$.
• Friction: $F_f = \mu F_N$, opposing sliding. Static friction adjusts up to a maximum $\mu_s F_N$; kinetic friction $\mu_k F_N$ acts once sliding starts. Compare the applied force with $\mu_s F_N$ to decide whether motion begins.

The Reference Tables print $F_g = mg$ and $F_f = \mu F_N$, plus a table of friction coefficients; the normal-force expressions are recall.

Free-body diagrams and equilibrium

A free-body diagram shows only the forces acting on the chosen object, as labelled arrows from a point. From it, you either apply Newton's second law (if the object accelerates) or the equilibrium conditions $\sum F_x = 0$ and $\sum F_y = 0$ (if it is at rest or at constant velocity). Resolve angled forces into components first, with $F_x = F\cos\theta$ and $F_y = F\sin\theta$ for an angle from the horizontal; on an incline, tilt the axes so the weight splits into $mg\sin\theta$ along the slope and $mg\cos\theta$ perpendicular to it.

Check your knowledge

A mix of recall, calculation and reasoning questions covering the forces module. Attempt them under timed conditions, then check against the solutions.

1. State Newton's first law and say what measures inertia. (2 marks)
2. A $5.0$ kg object has a net force of $20.$ N. Calculate its acceleration. (2 marks)
3. Explain why action-reaction forces do not cancel. (2 marks)
4. A $7.0$ kg object rests on a level floor. Calculate its weight and the normal force ($g = 9.81$ m/s squared). (2 marks)
5. State the equation for friction and define each symbol. (2 marks)
6. A box needs $60.$ N to start sliding but only $45$ N to keep sliding. State which coefficient is larger, static or kinetic. (1 mark)
7. State the two conditions for an object to be in equilibrium. (2 marks)
8. A $3.0$ kg object on a level floor has $\mu_k = 0.20$. Calculate the kinetic friction force ($g = 9.81$ m/s squared). (2 marks)
9. State what happens to acceleration if the net force doubles and the mass is unchanged. (1 mark)
10. A $25$ N lamp hangs at rest from one vertical cord. State the tension in the cord. (1 mark)