For the following parts of this problem, use the parallel axis theorem:a. Suppose a uniform slender rod has length L and mass M. The moment of inertia of therod about an axis that is perpendicular to the rod and that passes through its center ofmass is given by Icm =ml?. Find the moment of inertia through the end of the rod.12b. Suppose you have a uniform cube of mass m with edges of length a. The moment ofinertia above an axis through its center of mass and perpendicular to one of its faces isgiven by ICM =ma?. Find the moment of inertia through its edge (see figure below).%3Dр-аxisFigure 2. Cube rotating along an edge.

In the given question We use the parallel axis theorem and find the value of given parts.

For the following parts of this problem, use the parallel axis theorem: a. Suppose a uniform slender rod has length L and mass M. The moment of inertia of the rod about an axis that is perpendicular to the rod and that passes through its center of mass is given by IcM =ml?. Find the moment of inertia through the end of the rod. b. Suppose you have a uniform cube of mass m with edges of length a. The moment of inertia above an axis through its center of mass and perpendicular to one of its faces is given by IcM =ma?. Find the moment of inertia through its edge (see figure below). р-ахis Figure 2. Cube rotating along an edge.

For the following parts of this problem, use the parallel axis theorem: a. Suppose a uniform slender rod has length L and mass M. The moment of inertia of the rod about an axis that is perpendicular to the rod and that passes through its center of mass is given by IcM =ml?. Find the moment of inertia through the end of the rod. b. Suppose you have a uniform cube of mass m with edges of length a. The moment of inertia above an axis through its center of mass and perpendicular to one of its faces is given by IcM =ma?. Find the moment of inertia through its edge (see figure below). р-ахis Figure 2. Cube rotating along an edge.

College Physics

11th Edition

ISBN:9781305952300

Author:Raymond A. Serway, Chris Vuille

Publisher:Raymond A. Serway, Chris Vuille

Chapter1: Units, Trigonometry. And Vectors

Section: Chapter Questions

Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...

See similar textbooks

Similar questions

The wheel of radius R shown below consists of a hoop of massm and two thin rods, each of mass M. Calculate the moment of inertia of the wheel about an axis going through its center, perpendicular to the plane of the hoop, for the values listed below. Express your answer in kg m2 to three significant figures. R= 2.28 m m = 0.372 kg M= 0.288 kg
Two forces are acting on the beam which is pinned at the point O. a) Draw the free body diagram showing all forces. b) Determine the magnitude and direction of the resultant moment produced by the forces about point O. You can get the values of F (N), Q (N), X (m), d(m) and a (deg) from Table 1. F (N) 20 Q (N) F=675 //Q=125//x=9//%3D0.25//deg%3D20
A uniform bar has two small balls glued to its ends. The bar is 1.9 m long and has mass 1.5 kg, while the balls each have mass 0.5 kg and can be treated as point masses. Find the moment of inertia of this combination about an axis perpendicular to the bar and through one of the balls. the answer's unit is. Needs Complete typed solution with 100 % accuracy.
A force F = 71 N i acts on an object at a point (x0, y0) = (2.8 m, 2.2 m) as shown in the figure. What is the magnitude of the torque generated by this force about the origin? What is the magnitude of the torque generated by this force about the point (x, y) = (1.1 m, 0.9 m)? Suppose the object is free to rotate about the z axis. If the object has a moment of inertia I = 61.0 kg*m2 for rotation about the z axis, what is the magnitude of the angular acceleration of the object due to the application of the force F?
Consider a sphere of mass m and radius a, and centroidal axes x, y, and z. If the moment of inertia about the z-axis is known, which of the following equations correctly gives Iz', the moment of inertia about z'-axis - an axis parallel to z-axis and intersects (a,0,0)? a. Iz^2+Iz^2=1 b.Iz'=Iz-0.5ma^2 c. Iz'=Iz-4ma^2 d.Iz'=Iz+ma^2
A uniform thin rod of mass M = 3.37 kg pivots about an axis through its center and perpendicular to its length. Two small bodies, each of mass m = 0.219 kg, are attached to the ends of the rod. What must the length L of the rod be so that the moment of inertia of the three-body system with respect to the described axis is I = 0.975 kg-m? ? L = m M. m m L
9. The figure at right depicts the following situation: a thin uniform rod of length L = 3.0 m and mass M = 4.0 kg is free to pivot about a frictionless axle parallel to the z-axis and passing through its midpoint. The moment of inertia of the rod about the axle is =MI². Initially the rod is at rest, hanging vertically. A small clay ball of mass m = 1.0 kg is shot at the rod with velocity = (1.0"), and it impacts the rod at a distance L/3 below the pivot point. The clay ball sticks to the rod, and they both swing together in an upward arc. If the putty ball swings to a final maximum height h above the point where it first struck the rod, what is the height h? A) 0.003 m B) 0.013 m C) 0.027 m D) 0.043 m E) 0.067 m
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
2. Which of the following equations gives the mass moment of inertia of a thin homogenous rectangular plate with mass m base b, and height h, about the centroidal x-axis? h - b - A. 1/2mbh B. 1/2mh² c. mh² D. /mbh X
please solve symbolically before using numbers
Item 5 A uniform bar has two small balls glued to its ends. The bar is 3.00 m long and with mass 2.00 kg, while the balls each have mass 0.500 kg and can be treated as point masses. For related problem-solving tips and strategies, you may want to view a Video Tutor Solution of An abstract sculpture. Part A Find the moment of inertia of this combination about an axis perpendicular to the bar through its center. Express your answer in kilogram-meters squared. I = Submit Part B I = Submit "ΠΙ ΑΣΦ Part C 1 Request Answer Find the moment of inertia of this combination about an axis perpendicular to the bar through one of the balls. Express your answer in kilogram-meters squared. ΕΠΙ ΑΣΦ 1 ? Request Answer ? kg - m² ? kg-m² Find the moment of inertia of this combination about an axis parallel to the bar through both balls. Express your answer in kilogram-meters squared. IVE ΑΣΦ 3 Review
1. A satellite is spinning at 6 rev/s. The satellite consists of a main body in the shape of a sphere of radius 2 m and a mass of 800 kg, and two antennas projecting out from the surface of the main body that can be approximated with rods of length 3 m each and mass 10 kg. The antennas lie in the plane of rotation. See the figure below. M, L Ms R M₁L