An object of negligible size moves in a circular path of radius 20 m with 90 RPM. Find its radial acceleration.

(II) For each of the cases described below, sketch and label the total acceleration vector, the radial acceleration vector, and the tangential acceleration vector.

(a) A car speeds up as it rounds a curve of constant radius.

(II) For each of the cases described below, sketch and label the total acceleration vector, the radial acceleration vector, and the tangential acceleration vector.

(b) A car is going a constant 65 km/h as it rounds a curve of constant radius.

(II) For each of the cases described below, sketch and label the total acceleration vector, the radial acceleration vector, and the tangential acceleration vector.

(c) A car slows down while rounding a curve of constant radius.

A large disc of radius 10 m initially at rest takes 200 full revolutions to reach 30 RPM. Calculate the total linear acceleration of a point at half way between the disc's center and its edge, once the disc reaches 30 RPM. (You may assume it continues accelerating past that point)

(III) An object of mass m is constrained to move in a circle of radius r. Its tangential acceleration as a function of time is given by a_tan = b + ct² , where b and c are constants. If v = v₀ at t = 0 , determine the tangential and radial components of the force, F_tan and F_R, acting on the object at any time t > 0 .