Short on time? This page is the recap. For explanations, graphs and worked examples, use the full study guide. This is the algebra-based course: no calculus is needed.
Recap
- The net force ΣF is the vector sum of every force exerted on the system. Third-law partners act elsewhere and are not included.
- Translational equilibrium: ΣF = 0.
- Newton’s first law: if ΣF = 0, the velocity stays constant (same speed, same direction). The reverse is also used: constant velocity tells you ΣF = 0.
- Forces can be balanced along one axis but not the other. Only the velocity component along the unbalanced direction changes.
- Inertia is the tendency of an object to keep its velocity. Objects slow down only because a force such as friction acts.
- An inertial frame is one in which the first law is observed to hold. An accelerating frame (a braking bus) is not inertial.
Key relationships
| Relationship | Meaning | Use it to |
|---|---|---|
| ΣF = F₁ + F₂ + … | vector sum of forces on the system | find the net force |
| ΣF = 0 | translational equilibrium | test for constant velocity |
| ΣF_x = 0, ΣF_y = 0 | one equation per axis | solve for unknown forces |
| ΣF = 0 ⇔ v constant | first law (with its reverse) | link forces and motion |
| v–t graph flat ⇔ ΣF = 0 | zero slope, zero acceleration | sketch or read graphs |
Assumptions behind the numbers
- The ground is an inertial frame unless a question says otherwise.
- Strings and cords are ideal: one tension along each one.
- Weight near Earth’s surface is F_g = mg with g = 9.8 m/s².
- Air resistance is ignored unless it is mentioned.
Mistakes to avoid
- “Moving means a force is pushing it forwards.” Constant velocity needs zero net force.
- “Equilibrium means at rest.” A lift rising at a steady speed is in equilibrium.
- “v = 0 means equilibrium.” A ball at the top of its flight has ΣF = mg downward.
- Writing one equation for a 2D problem. You need ΣF_x = 0 and ΣF_y = 0.
- Assuming F_N = mg. An angled pull or push changes the normal force.
- Adding a third-law partner into ΣF. Only forces on the chosen system count.
- Expecting velocity to “return” after a force stops. It stays at its new value.
Quick self-check
- Three horizontal forces act on a puck: 5.0 N east, 5.0 N west and 2.0 N north. Is the puck in equilibrium? (No. ΣF = 2.0 N north; its velocity changes towards the north, while its east–west velocity stays the same.)
- A 2.0 kg bag hangs at rest from an ideal string. What is the tension? (19.6 N, equal to mg.)
- In a lift moving down at a steady speed, a coin lies at rest on the floor. Is the lift an inertial frame? (Yes. It moves at constant velocity, and the coin obeys the first law in it.)
Next: practice questions.