Forest UCM NLM Oscilations

Skate boarder in Half pipe

Consider a frictionless skateboard released from the top of a semi-circle (half pipe) and oriented to fall directly towards the bottom. The semi-circle has a radius [math]R[/math] and the skateboard has a mass [math]m[/math].

Note: because the skateboard is frictionless, its wheels are not going to turn.

Step 1: System

The skateboard of mass [math]m[/math] is the system.

Step 1: Coordinate system

Polar coordinate may be a good coordinate system to use since the skateboard's motion will be along the half circle.

300 px

Step 4: External Force vectors

[math]\vec{F}_g = -mg \cos \theta \hat{r} - mg \sin \theta \hat{\phi}[/math]

[math]\vec{N} = N \hat{r}[/math]

Step 5: apply Netwon's 2nd Law

\sum \vec{F}_ext = \vec{F}_g + \vec{N} = m \left ( \right )

Forest_UCM_NLM#Oscillatiions