5. Calculate the moment of inertia of a thin rod of length L with a linear mass density given by: x4 λ(x) = 20 (1) λο The rod is rotated around its center as shown below. Quote your answer in terms of M, L, and any necessary numerical constants. x = 0 corresponds to the midpoint of the rod. L x

5. Calculate the moment of inertia of a thin rod of length L with a linear mass density given by: x4 λ(x) = 20 (1) λο The rod is rotated around its center as shown below. Quote your answer in terms of M, L, and any necessary numerical constants. x = 0 corresponds to the midpoint of the rod. L x

Physics for Scientists and Engineers, Technology Update (No access codes included)

9th Edition

ISBN:9781305116399

Author:Raymond A. Serway, John W. Jewett

Publisher:Raymond A. Serway, John W. Jewett

Chapter10: Rotation Of A Rigid Object About A Fixed Axis

Section: Chapter Questions

Problem 10.3OQ: A wheel is rotating about a fixed axis with constant angular acceleration 3 rad/s2. At different...

See similar textbooks

Similar questions

A wheel is rotating about a fixed axis with constant angular acceleration 3 rad/s2. At different moments, its angular speed is 2 rad/s, 0. and +2 rad/s. For a point on the rim of the wheel, consider at these moments the magnitude of the tangential component of acceleration and the magnitude of the radial component of acceleration. Rank the following five items from largest to smallest: (a) |at| when = 2 rad/s, (b)|ar| when = 2 rad/s, (c)|ar| when = 0, (d) |at| when = 2 rad/s, and (e) |ar| when = 2 rad/s. If two items are equal, show them as equal in your ranking. If a quantity is equal to zero, show that fact in your ranking.
A system consists of a disk of mass 2.0 kg and radius 50 cm upon which is mounted an annular cylinder of mass 1.0 kg with inner radius 20 cm and outer radius 30 cm (see below). The system rotates about an axis through the center of the disk and annular cylinder at 10 rev/s. (a) What is the moment of inertia of the system? (b) What is its rotational kinetic energy?
Find the net torque on the wheel in Figure P10.23 about the axle through O, taking a = 10.0 cm and b = 25.0 cm. Figure P10.23
Figure OQ10.6 shows a system of four particles joined by light, rigid rods. Assume a = b and M is larger than m. About which of the coordinate axes does the system have (i) the smallest and (ii) the largest moment of inertia? (a) the x axis (b) the y axis (c) the z axis, (d) The moment of inertia is the same small value for two axes, (e) The moment of inertia is the same for all three axes.
A system of point particles is rotating about a fixed axis at 4 rev/s. The particles are fixed with respect to each other. The masses and distances to the axis of the point particles are m1=0.1kg , r1=0.2m , m2=0.05kg , r2=0.4m , m3=0.5kg , r3=0.01m . (a) What is the moment of inertia of the system? (b) What is the rotational kinetic energy of the system?
A baseball catcher extends his arm straight up to catch a fast ball with a speed of 40 m/s. The baseball is 0.145 kg and the catcher’s arm length is 0.5 m and mass 4.0 kg. (a) What is the angular velocity of the arm immediately after catching the ball as measured from the arm socket? (b) What is the torque applied if the catcher stops the rotation of his arm 0.3 s after catching the ball?
A playground merry-go-round of radius R = 2.00 m has a moment of inertia I = 250 kg m2 and is rotating at 10.0 rev/min about a frictionless, vertical axle. Facing the axle, a 25.0-kg child hops onto the merry-go-round and manages to sit down on the edge. What is the new angular speed of the merry-go-round?
Check Your Understanding What is the moment of inertia of a cylinder of radius R and mass m about an axis through a point on the surface, as shown below? A uniform thin disk about an axis through the center Integrating to find the moment of inertia of a two-dimensional object is a little bit trickier, but one shape is commonly done at this level of study—a uniform thin disk about an axis through its center (Figure 10.27). Figure 10.27 Calculating the moment of inertia for a thin disk about an axis through its center.
Rigid rods of negligible mass lying along the y axis connect three particles (Fig. P10.18). The system rotates about the x axis with an angular speed of 2.00 rad/s. Find (a) the moment of inertia about the x axis, (b) the total rotational kinetic energy evaluated from 12I2, (c) the tangential speed of each particle, and (d) the total kinetic energy evaluated from 12mivi2. (e) Compare the answers for kinetic energy in parts (b) and (d). Figure P10.18
Review. As shown in Figure P10.77, two blocks are connected by a string of negligible mass passing over a pulley of radius r= 0.250 m and moment of inertia I. The block on the frictionless incline is moving with a constant acceleration of magnitude a = 2.00 m/s2. From this information, we wish to find the moment of inertia of the pulley. (a) What analysis model is appropriate for the blocks? (b) What analysis model is appropriate for the pulley? (c) From the analysis model in part (a), find the tension T1(d) Similarly, find the tension T2. (e) From the analysis model in part (b), find a symbolic expression for the moment of inertia of the pulley in terms of the tensions T1 and T2. the pulley radius r, and the acceleration a. (f) Find the numerical value of the moment of inertia of the pulley.
A rigid body with a cylindrical cross-section is released from the top of a 30 incline. It rolls 10.0 m to the bottom in 2.60 s. Find the moment of inertia of the body In terms of its mass m and radius r.
A horizontal disk with moment of inertia I1 rotates with angular speed 1 about a vertical frictionless axle. A second horizontal disk having moment of inertia I2 drops onto the first, initially not rotating but sharing the same axis as the first disk. Because their surfaces are rough, the two disks eventually reach the same angular speed . The ratio /l is equal to (a) I1/I2 (b) I2/I1 (c) I1/( I1 + I2) (d) I2/( I1 + I2)