I'm currently doing an extended project qualification and my topic is to form an equation which maximizes the probability of the ball landing on a point marked with a red pen on the ball.
Assuming that the ball is exactly spherical, with a diameter of 'd'. The ball is rolled of a curved downwards surface to make friction negligible . The ball moves down a vertical distance of height H_t and is in contact with the surface for a distance of twice the circumference of the ball. It starts rotating when the red dot touches the surface and rolls off when the red dot touches the surface. So as sum of energy is conserved KE = GPE V_final when the ball leaves the surface is V_final = sqrt(2gH_t). The ball then undergo projectile motion with horizontal speed of sqrt(2gH_t) and moves a horizontal distance of R. And it moves down a vertical distance of H_f as it reaches the ground. Using the idea of Torque = rotational inertia x angular acceleration is it possible to determine how many times the ball will spin before it touches the ground. or for a time of T seconds which can be calculated by the verticle distance.
I need some recommendations of physics concepts I should look at for example, newton's second law of rotation, and etc to be able to determine this. Also, i want to apply air resistance to the system.
Given area of the sphere incontact with the air is, pi x d^2 , Drag coefficient is; C_d Density of air is ; Rho
My plan is once i get torque = rotational inertia x angular acceleration, I can integrate both sides twice to get angular displacement setting boundary conditions