Problem Statement A carousel with a radius of R = 3.0 meters is initially at rest. It is then given a constant angular acceleration = 0.06 rad/s. A. Sketch the physical situation and label your sketch with appropriate quantities from the problem statement. Make a table of known/given information and unknown/wanted information (this may involve reading the rest of the problem before starting). List any physical assumptions you will be making to solve the problem. B. What is the angular velocity of the carousel after t = 8.0 s? What is the linear velocity of a child located at 2.5 meters from the center of the carousel after t = 8.0 s? What is the tangential acceleration of the child at that time? What is the child's radial acceleration at that time? C. Determine the magnitude and direction of the child's total acceleration vector after 8.0 s. Add this vector to your diagram above and show the directions of the radial and tangential components. D. How many rotations does the carousel complete in the first 8 seconds? E. Assess the validity of your work in the following ways: 1. Check the physical units of your expressions in part B-D. What are the units of angle? What are the dimensions of angle? What is the difference? 2. What fraction of a g-force is the child's acceleration? Is this reasonable for a carousel? 2