Serway & Jewett — Rotation of a Rigid Object about a Fixed Axis: Problem 12

Review. A small object with mass \(4.00 \text{ kg}\) moves counterclockwise with constant angular speed \(1.50 \text{ rad/s}\) in a circle of radius \(3.00 \text{ m}\) centered at the origin. It starts at the point with position vector \(3.00 \hat{\mathbf{i}} \text{ m}\). It then undergoes an angular displacement of \(9.00 \text{ rad}\). (a) What is its new position vector? Use unit-vector notation for all vector answers. (b) In what quadrant is the particle located, and what angle does its position vector make with the positive \(x\) axis? (c) What is its velocity? (d) In what direction is it moving? (e) What is its acceleration? (f) Make a sketch of its position, velocity, and acceleration vectors. (g) What total force is exerted on the object?