# maths

posted by
**gemma**
.

3. Suppose that a particle moves in a plane with trajectory given by the polar equation r=2bsintheta for some constant b > 0.Show that this can be written in Cartesian coordinates as,x^2 + (y-b)^2 = b^2;This is the equation for a circle of centre (0; b) and radius b. Suppose that the transverse component of the acceleration is zero Prove that r^2theta = h is constant. Assuming that r 6= 0, show that r. = 2bhr^-2 cos(theta) and hence find r..

Use your answers to (b) to show that the radial component of the

acceleration is -8b^2h^2r^-5.

recall that r^2 = x^2 + y^2 and y = r sin(theta).