Short on time? This page is the recap for the calculus-based course. For diagrams and worked examples, use the full study guide.
Recap
- The net force is the vector sum of all forces exerted on the system. Partners on other objects stay out.
- Translational equilibrium: ΣF = 0. Apply it as separate component equations.
- First law: if ΣF = 0, the system’s velocity stays constant in size and direction. Rest is one case.
- Constant velocity means a = dv/dt = 0 and a straight-line position graph.
- Forces can balance along one axis and not another. Only the velocity component along the unbalanced direction changes.
- An inertial frame is one in which the first law is observed to hold. Frames moving at constant velocity relative to it are inertial too; accelerating frames are not.
Key relationships
| Idea | Statement | Use it to |
|---|---|---|
| Net force | ΣF = F₁ + F₂ + … | combine forces by components |
| Equilibrium | ΣF_x = 0, ΣF_y = 0 (ΣF_z = 0) | find up to two unknowns in 2D |
| First law | ΣF = 0 ⇔ v constant | link forces to motion graphs |
| One axis balanced | ΣF_x = 0 ⇒ v_x constant | treat each axis separately |
| Inertial frame | first law holds | choose where to analyse from |
Assumptions behind the numbers
- g = 9.8 m/s² near Earth’s surface.
- The ground is treated as an inertial frame unless told otherwise.
- “At rest” or “constant velocity” in a question is your signal that ΣF = 0.
Mistakes to avoid
- Motion needs a force. Only a change in velocity needs a net force.
- Equilibrium = rest. Constant velocity is equilibrium too.
- v = 0 for an instant = equilibrium. Check the forces, not the velocity.
- Constant speed while turning = equilibrium. Direction is changing, so ΣF ≠ 0.
- Mixing components. Keep x and y equations separate, with signs.
- Including third-law partners in ΣF. They act on other objects.
- Reasoning from inside an accelerating vehicle. Switch to the ground frame.
Quick self-check
- Two forces on a puck are (3.0, 0) N and (0, 4.0) N. What third force gives equilibrium, and how big is it? ((−3.0, −4.0) N, size 5.0 N.)
- A crate slides across a floor at constant velocity while a worker pushes it horizontally with 60 N. What is the friction force? (60 N, opposite to the push, because ΣF_x = 0.)
- x(t) = 4.0t and y(t) = 2.0 + 1.5t² (m). In which direction are the forces balanced? (Along x only: v_x is constant, v_y changes.)
Next: practice questions.