The acceleration of a particle in a fixed coordinate system in terms of it's position in a translating and rotating coordinate system (primed) is: a = a_0 + w(dot) x r' + w x (w x r') + 2w x r(dot)' + r(double dot)'
where a_o is the acceleration of the origin of the primed system, w is the angular velocity of the primed system, and r' is the particle position in the primed system. The first three terms are the acceleration of the point in the moving frame coinciding with the particle, the term 2w x r(dot)' is the Coriolis acceleration, and the last term is the acceleration of the particle relative to the moving frame.
Consider a wheel of radius b rolling with constant speed v_0 around a circular track of radius R. Choose a moving coordinate system with origin O at the center of the wheel, an x' axis that points toward the center of the circular track, a z' axis that remains vertical, and a y' axis that points in the direction opposite the wheel's forward velocity.
1. Find the acceleration relative to the ground of the highest point of the wheel.
2. Find the acceleration relative to the ground of the point at the very front of the wheel.
a = acceleration, w = omega, r' = r prime, r(dot) = a dot above r, r(double dot) = two dots above r