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## High school physics

### Course: High school physics>Unit 3

Lesson 6: Angled forces

# Angled forces review

Review the key skills for angled forces, such as how to break down forces into the horizontal and vertical components.

## How to write force equations using components of an angled force

Sometimes forces are angled and do not point along the coordinate axes. Let's analyze the specific example shown in Figure 1.
An angled force can be broken down to horizontal and vertical components (see Figure 2 below). This allows us to apply Newton’s second law to the forces in the horizontal and vertical directions separately.
The components of the applied force F are:
\begin{aligned} F_x &= F\cos\theta \\\\ &\text{and} \\\\ F_y &= F\sin\theta \end{aligned}

### Analyzing forces in the horizontal direction

If our box in Figure 1 experiences no friction, the only force acting horizontally is the horizontal component of F, comma, F, start subscript, x, end subscript. We can apply Newton’s second law to the horizontal direction and write F, start subscript, x, end subscript in terms of F and theta.
m, a, start subscript, x, end subscript, equals, F, start subscript, x, end subscript, equals, F, cosine, theta

### Analyzing forces in the vertical direction

If the box stays on the table, the vertical component of F, comma, F, start subscript, y, end subscript acts vertically along with weight down and normal force up to produce zero vertical acceleration. We can apply Newton’s second law to the vertical direction and write F, start subscript, y, end subscript in terms of F and theta.
\begin{aligned}ma_y&=F_y \\\\ 0 &= F\sin\theta + F_N - F_g\end{aligned}