A motorcycle/rider combination has a center of mass that is half a meter diagonally upward and in front of the point of contact between the wheel and the road at an angle of 30 degrees when the bike is level. What acceleration is necessary to keep the bike tilted up stably another thirty degrees?
If I read this correctly, you have two competing torques: weight pulling the cm down, and inertia pulling it back, acting at the base of the wheel. Let L be the distance from cm to the contact point. Summing moments about that point..
mg*L*sin30-ma*L*cos30=0
solving for a..
a=g*tan30