# W r t f n 750º 442 rotational dynamics 32 reasoning

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W R T F N 75.0º
442 ROTATIONAL DYNAMICS 32. REASONING For a rigid body rotating about a fixed axis, Newton's second law for rotational motion is given as I τ α = (Equation 9.7), where I is the moment of inertia of the body and α is the angular acceleration. In using this expression, we note that α must be expressed in rad/s 2 . ______________________________________________________________________________
33. REASONING The moment of inertia of the stool is the sum of the individual moments of inertia of its parts. According to Table 9.1, a circular disk of radius R has a moment of inertia of 2 1 disk disk 2 I M R = with respect to an axis perpendicular to the disk center. Each thin rod is attached perpendicular to the disk at its outer edge. Therefore, each particle in a rod is located at a perpendicular distance from the axis that is equal to the radius of the disk. This means that each of the rods has a moment of inertia of I rod = M rod R 2 .
34. REASONING According to Newton’s second law for rotational motion, Σ τ = I α , angular acceleration α of the blades is equal to the net torque Σ τ applied to the blades divided by their total moment of inertia I , both of which are known. the
35. REASONING Newton’s second law for rotational motion (Equation 9.2) indicates that the net external torque is equal to the moment of inertia times the angular acceleration. To determine the angular acceleration, we will use Equation 8.7 from the equations of rotational kinematics. This equation indicates that the angular displacement θ is given by 2 1 0 2 t t θ ω α = + , where ω 0 is the initial angular velocity, t is the time, and α is the angular acceleration. Since both wheels start from rest, ω 0 = 0 rad/s for each. Furthermore, each
Chapter 9 Problems 443 0 1
36. REASONING The ladder is subject to three vertical forces: the upward pull of the painter on the top end of the ladder, the upward normal force F N that P