Newton’s second law for rotational motion Equation...

Newton’s second law for rotational motion Equation

Fire escape A unique fire escape for a three-story house is shown in Figure P8.39. A 30-kg child grabs a rope wrapped around a heavy flywheel outside a bedroom window. The flywheel is a 0.40-m-radius uniform disk with a mass of 120 kg. (a) Make a force diagram for the child as he moves downward at increasing speed and another for the flywheel as it turns faster and faster. (b) Use Newton’s second law for translational motion and the child force diagram to obtain an expression relating the force that the rope exerts on him and his acceleration. (c) Use Newton’s second law for rotational motion and the flywheel force diagram to obtain an expression relating the force the rope exerts on the flywheel and the rotational acceleration of the flywheel. (d) The child’s acceleration a and the flywheel’s rotational acceleration a are related by the equation a = ra, where r is the flywheel’s radius. Combine this with your equations in parts (b) and (c) to determine the child’s acceleration and the force that the rope exerts on the wheel and on the child.