dynamics, polar coordinate system

bartieshaw

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

Meir Achuz

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).