i have been set the following question theta = 3r^2 find the magnitude of the acceleration when r=0.8 m dr/dt = 4ms^-1 d^2r/dt^2 = 12 ms^-2 my working followed the process of calculating angular velocity with these conditions and angular acceleration with these conditions then plugging them into the acceleration formula for a polar coordinate system. when doing this i get a(radial) = -282.912 ms^-2 (componant along the radius) a(theta) = 218.88 ms^-2 (componant perpendicular to radius) using pythagoras to calculate the magnitude of the resultant acceleration i get a value 357.7 ms^-2 a value my dynamics lecturer is prompt to tell me is WRONG. perhaps someone can help me...PLEASE
Your numbers are wrong. I don't see how you could get them. The radial acceleration is GIVEN to you as 12 m/s^2. You have to relate d^2theta/dt^2 to d2r/dt^2 by differentiating the equation theta=3r^2 twice. Then rd^2theta/dt^2 s gives a(theta).