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## Class 11 Physics (India)

### Course: Class 11 Physics (India)>Unit 9

Lesson 8: Inclined planes

# Inclined planes review

Review the key concepts and skills for inclined planes, including how to write Newton's second law for forces parallel and perpendicular to the incline.

## Key terms

Term (symbol)Meaning
Inclined planeA tilted surface, sometimes called a ramp or incline.

## How to write Newton’s second law for forces on an incline

1) Draw a free body diagram for the object (see Figure 3). Remember to rotate the coordinate axes to align with the incline (see Figure 1 below).
If there is any acceleration, it will typically be along the parallel axis (labeled $\parallel$) of the incline.
The perpendicular axis (labeled $\perp$) typically has no acceleration and ${a}_{\perp }=0$.
2) Write the Newton’s second law statement for the direction of interest.
$m{a}_{\perp }=\Sigma {F}_{\perp }$ OR $m{a}_{\parallel }=\mathrm{\Sigma }{F}_{\parallel }$
The perpendicular direction’s equation simplifies because ${a}_{\perp }=0$:
$\begin{array}{rl}m\left(0\right)& =\mathrm{\Sigma }{F}_{\perp }\\ \\ 0& =\mathrm{\Sigma }{F}_{\perp }\end{array}$
3) Substitute the sum of all the forces acting in the direction of interest ($\perp$ or $\parallel$) for $\mathrm{\Sigma }F$. Use your free body diagram to identify which forces are acting in the direction of interest.
Sometimes a force is completely aligned in the parallel or perpendicular direction like normal force and friction.
Some forces have components in both the parallel and perpendicular direction, such as the force of gravity. In that case, the force should be broken down into the parallel and perpendicular components (see Figure 2 below) for substitution in the net force equations.
The parallel and perpendicular components of weight are (Figure 2):
$\begin{array}{rl}{F}_{g\perp }& ={F}_{g}\mathrm{cos}\theta \\ \\ {F}_{g\parallel }& ={F}_{g}\mathrm{sin}\theta \end{array}$

## Common mistakes and misconceptions

People forget the force directions. The diagram below shows the forces on an object resting on an incline.
• Weight ${F}_{g}$ is straight down.
• Normal force ${F}_{N}$ pushes perpendicular to the incline.
• Friction ${F}_{f}$ acts parallel to the incline.