Skateboarder's tang. and radial acceleration

[lewis198]

This was actually an old problem I got wrong.

Homework Statement

) A skateboarder rolls down a semicircular ramp (half pipe) of radius 4.0m, starting from rest at the top of the ramp (figure 1). Assuming the surface to be frictionless, calculate his radial and tangential acceleration when he is 2.0m below the top of the ramp. What is the resultant acceleration vector (magnitude and direction, given as an angle to the horizontal) at this point?

Homework Equations

The Attempt at a Solution

I equated the radial acceleration to gcos(arccos(2/4)) and the tangential to gsin(arccos(2/4))
where have I gone wrong here? to me it seems right.

 

[rl.bhat]

Radial acceleration is the resultant of centripetal acceleration and the component of mg along the radius.

 

[lewis198]

why are they both not opposite and equal?

 

[lewis198]

Radial acceleration is the resultant of centripetal acceleration and the component of mg along the radius.

Why is the radial acceleration not equal and opposite component of mg along the radius?

Isn't the normal force, in this case the component of mg along the radius providing the radial acceleration?

 

[Doc Al]

The normal force does not equal the radial component of mg. (If it did the radial acceleration would be zero.)