Short on time? This page is the recap for the calculus-based course (separate from Physics 1). For explanations, diagrams and worked examples, use the full study guide.
Recap
- A force is a vector describing an interaction between two objects or systems. Name both: “F_T, cable on crate”.
- An object or system cannot exert a net force on itself. Internal forces cancel in pairs.
- Contact forces (normal, friction, tension, spring, drag) are the large-scale effect of electric forces between atoms. Long-range forces, such as gravity, need no contact.
- A free-body diagram shows only the forces exerted on the chosen system by its environment.
- If a force changes with time, each diagram is a snapshot at one instant.
Key relationships
| Rule or result | Notes |
|---|---|
| Dot = center of mass | The system is treated as if all its mass were there |
| One straight arrow per force, starting on the dot | Label “by what, on what” |
| Same-direction forces side by side | Never merged, never overlapping |
| No components on the diagram | Split forces in your working |
| ΣF = F₁ + F₂ + … (add by components) | Unit-vector notation: ΣF = (ΣF_x) i + (ΣF_y) j |
| Gravity on a slope of angle θ | mg sin θ down the slope; mg cos θ into the slope |
| F_g = mg | g = 9.8 m/s² near Earth’s surface |
Assumptions behind the numbers
- g = 9.8 m/s² near Earth’s surface. Strings and cables are light, so they pull along their length.
- “Smooth” means friction is negligible. “Steady velocity” or “at rest” means the forces balance (Topic 2.4).
- Axes are stated each time, with one axis along the motion.
Mistakes to avoid
- Drawing components as extra arrows on the diagram.
- Merging two same-direction forces into one arrow.
- “Force of motion”, “inertia” or “ma” arrows. None of these has a “by what”.
- Forces the system exerts on other objects. They belong on those objects’ diagrams.
- Internal forces on a system diagram. They cancel; leave them off.
- N = mg every time. Find N from the diagram; ropes, pushes and slopes change it.
- Horizontal axes on a slope, which makes extra components.
Quick self-check
- A hand presses down with 5.0 N on a 2.0 kg book resting on a table. What is the normal force from the table? (19.6 + 5.0 = 24.6 N, about 25 N)
- A 10 kg box sits on a 40° slope. Find the components of gravity along and into the slope. (63 N down the slope; 75 N into it)
- What exerts the forward force on a sprinter leaving the blocks? (The blocks and ground, pushing on her feet. Her muscles are internal to the system “sprinter”.)
Next: practice questions.