1. Use slide show mode (press F5) for animations.
Inclined Planes
Label the direction of N and mg. N θ mg
Use slide show mode (press F5) for animations.

2. Inclined Planes
Mark the direction of acceleration a. N a θ mg

3. Inclined Planes
Choose the coordinate system with x in the same or opposite direction of acceleration and y perpendicular to x. y N x a θ mg

4. Inclined Planes
Now some trigonometry y N x a θ
90- θ mg θ

5. Inclined Planes Replace the force of gravity with its components.x a
mg sinθ
mg cosθ θ θ mg

6. Inclined Planes mg sinθ mg cosθ mg
Use Newton’s second law for both the x and y directions y N x a
mg sinθ
mg cosθ θ θ mg
The force and acceleration in the x-direction have a negative sign because they point in the negative x-direction.

7. Inclined Planes mg sinθ mg cosθ mg
Why is the component of mg along the x-axis –mgsinθ
Why is the component of mg along the y-axis –mgcosθ mg
mg sinθ θ
mg cosθ N a x y

8. Inclined Planes mg sinθ mg mg cosθ
Why is the component of mg along the x-axis: –mgsinθ
Why is the component of mg along the y-axis: –mgcosθ y N a
mg sinθ x θ θ mg
mg cosθ

9. Inclined Planes mg sinθ mg mg cosθ
Why is the component of mg along the x-axis: –mgsinθ
Why is the component of mg along the y-axis: –mgcosθ y N a
mg sinθ x θ θ mg
mg cosθ

10. Inclined Planes mg sinθ mg mg cosθ
Why is the component of mg along the x-axis: –mgsinθ
Why is the component of mg along the y-axis: –mgcosθ θ y
opposite N
sinθ = a
hypotenuse
adjacent
cosθ =
mg sinθ
hypotenuse x θ mg
mg cosθ