1. Consider a solid sphere and a solid disk with the same radius and the same mass. Explain why the solid disk has a greater moment of inertia than the solid sphere, even though it has the same overall mass and radius.
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- A cylindrical body has mass M and radius R. Can the mass be distributed within the body in such a way that its moment of inertia about its axis of symmetry is greater than MR2? Explain.Three solid spheres are attached to each other along the line joining their centers as shown in Figure 4. The spheres have the following masses and radii: , M2 = 10 kg M1 = 5 kg , M3 = 15 kg Rị = 2 m R2 = 3.2 m R3 = 4 m Calculate the moment of inertia of the system (three spheres) about the axis shown in the figure. M1 M2 M3 Figure 42. A hollow sphere of radius R = 0.15 m rolls without slipping on a horizontal surface. The moment of inertia of the sphere is I = 2MR²/3 = 0.040 kg.m², where M is the mass of the sphere. The sphere's total initial kinetic energy is 20 J. What is the initial translational speed of the center of the sphere?
- *58. Go A dragster starts from rest and accelerates down a track. Each tire has a radius of 0.320 m and rolls without slipping. At a distance of 384 m, the angular speed of the wheels is 288 rad/s. Determine (a) the linear speed of the dragster and (b) the magnitude of the angular acceleration of its wheels.68. Refer to Multiple-Concept Example 7 for insight into this problem. During a tennis serve, a racket is given an angular acceleration of magni- tude 160 rad/s². At the top of the serve, the racket has an angular speed of 14 rad/s. If the distance between the top of the racket and the shoulder is 1.5 m, find the magnitude of the total acceleration of the top of the racket.Computation. Consider a stick 1.00 m long and its moments of inertia about axes perpendicular to the stick's length and passing through two different points on the stick: first, a point at its center and second, a point 24 cm from one end. Calculate the ratio I2/11, the ratio of the second moment of inertia to the first. 55 Record your numerical answer below, assuming three significant figures. Remember to include a "_" as necessary. == O Search
- 4. A dumbbell consists of two 0.2-meter diameter spheres, each with a mass of 40 kg, attached to the ends of a 0.6-meter-long, 20 kg slender rod. .2 m .3 m .3 m .2 m 40 kg 20 kg 40 kg Figure 4 (a) Find out the moment of inertia of the dumbbell about the y axis and compare it with the moment of inertia about the z axis as shown in the figure. (b) Find out the moment of inertia of the dumbbell about the x axis. (c) Find out the moment of inertia of the dumbbell if the axis of rotation passes through the center of either of the spheres and perpendicular on the slender rod.Consider two identical disks. Would drilling a hole into the center of the first disk cause it to have a larger moment of inertia around the axis through the center and at right angles to the disk? Explain.An automatic dryer spins wet clothes at an angular speed of 4.7 rad/s. Starting from rest, the dryer reaches its operating speed with an average angular acceleration of 3.4 rad/s². How long does it take the dryer to come up to speed? i eTextbook and Media GO Tutorial Save for Later Attempts: 0 of 3 used Submit Answer SUPPORT C # $ 2 3 4 וום 205 % & ( 6 7 8 9 W e r t Y u i S d f 60 h K 0 4 Mar 26 P 9:30 US X
- *Chapter 10, Problem 31 ZYour answer is partially correct. Try again. A disk, with a radius of 0.25 m, is to be rotated like a merry-go-round through 200 rad, starting from rest, gaining angular speed at the constant rate 1 through the first 100 rad and then losing angular speed at the constant rate -1 until it is again at rest. The magnitude of the centripetal acceleration of any portion of the disk not to exceed 400 m/s2. (a) What is the least time required for the rotation? (b) What is the corresponding value of C1 ? (a) Number Units (b) Number Units Trad/s^2Multiple concept problem: A bike wheel having a moment of inertia of 0.09 kg-m2 has an initial angular speed of 3 rev/s and gradually comes to rest due to a frictional force. The frictional force is caused by a torque of 1.0 N-m. Assuming the angular deceleration remains constant during the entire period, determine how much time it would require for the wheel to come to a stop.A spherical shell with a mass of 1.6 kg and a radius of 0.35 m is rolling across the level ground with an initial angular velocity of 37.7 rad/s. It is slowing at an angular rate of 4 rad/s². What is its rotational kinetic energy after 4.4 s? The moment of inertia of a spherical shell is I = MR²