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A force at an angle can be split into two perpendicular components. Resolving forces into horizontal and vertical (or other) directions lets you apply Newton’s laws one direction at a time.
The big picture
Choose perpendicular axes and resolve every force, including weight. If a pulling force points upwards at an angle, its vertical component reduces the normal reaction. Setting the reaction equal to weight automatically is then incorrect. On a rough horizontal surface the friction bound depends on the new reaction. Resolve vertically before using the friction law, and ensure the reaction remains nonnegative so contact is maintained.
What you'll be able to do
A force at angle to a direction has a component along that direction and perpendicular to it.
Tip — The component ALONG the angle’s reference direction uses cos; the perpendicular one uses sin.
Choose perpendicular axes and resolve every force, including weight. If a pulling force points upwards at an angle, its vertical component reduces the normal reaction. Setting the reaction equal to weight automatically is then incorrect.
On a rough horizontal surface the friction bound depends on the new reaction. Resolve vertically before using the friction law, and ensure the reaction remains nonnegative so contact is maintained.
Think like an examiner
Common misconceptions
Key results to remember
Key takeaways
Test yourself
Answer a few questions, then review anything you missed.
Start with the quiz above to check the key ideas. You can also choose another topic from the practice library.