If you're seeing this message, it means we're having trouble loading external resources on our website.

If you're behind a web filter, please make sure that the domains *.kastatic.org and *.kasandbox.org are unblocked.

Main content

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.
Figure 1. Angled force acting on a box that rests on a table.
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.
Figure 2. Components of a force F at angle θ on box with mass m. The component Fx is in the horizontal direction, and Fy is in the vertical direction.
The components of the applied force F are:
Fx=FcosθandFy=Fsinθ

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,Fx. We can apply Newton’s second law to the horizontal direction and write Fx in terms of F and θ.
max=Fx=Fcosθ

Analyzing forces in the vertical direction

If the box stays on the table, the vertical component of F,Fy 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 Fy in terms of F and θ.
may=Fy0=Fsinθ+FNFg

Learn more

To see a worked example involving a force at an angle, see our video about tension forces on a box.
To check your understanding and work toward mastering these concepts, check out the exercise on forces at an angle.

Want to join the conversation?