Consider the system shown in the figure. Disk m, rolls without slip. a is defined as the displacement of mass mo and ispositive to the left. When x displaces in a positive direction, it rotates the disk (with moment of inertia J1 and radius R) by anangle 01. Use 0, to denote the rotation of the mass m, (a disk with moment of inertia J, and radius r2). Assume smalldisplacements (and hence small rotations). Use x as the coordinate to describe this system.mom2wwkSyntaxUse J[1],J[2], k[1].r[1].r[2],m[2] for J1 ,J9,k1.r1.r2 and m2. Use m[0] (m with subscript as the number zero) for mo-How many degrees of freedom does this system have?The system has 2 degrees of freedom - from the disk and cart that are on the horizontal surface plus the rotating disk onthe left.The system has 4 degrees of freedom: translation and roation of the first disk, rotation of the other disk and translation ofmass mo-O None of the other responses are correct.O The system has 3 degrees of freedom because there are 3 separate masses; two disks and mass mo.KinematicsWhen mass mo moves by a distance z, the cylinder with moment of inertia J, rotates by01 =When mass mn moves by a distance x, the cylinder with moment of inertia J,rotates byWhen mass mo moves by a distance x, the spring with stiffness k1 compresses by*k1

Answered: Image /qna-images/answer/ab336cf5-2ce0-4665-a2e9-091690476213.jpg

Answered: mo m2 | bartleby

Engineering

Mechanical Engineering

mo m2

Elements Of Electromagnetics

7th Edition

ISBN:9780190698614

Author:Sadiku, Matthew N. O.

Publisher:Sadiku, Matthew N. O.

ChapterMA: Math Assessment

Section: Chapter Questions

Problem 1.1MA

See similar textbooks

Similar questions

Consider a pulley system shown below. Assume there is no slip between the cord and the pulley. I is the mass moment of inertia of the pulley about its own centroidal axis. Find the equations of motion in terms of x. Select all that apply.
Two bars, each weighing 5.1 lb/ft, are welded together as shown in figure below. With A = 4.3 ft and B = 6.2 ft, find I, the moment of inertia with respect to the center of the mass in slug-ft2. A В Figure is from "Engineering Mechanic An Introduction to Dynamics", McGill and King.
Figure shows a mechanical system. The connecting link has moment of inertia J about its pivot point, and rotation angle is positive clockwise. Position of mass m is positive to the right. Both the angular and translational displacements are measured from the equilibrium position where all springs are undeflected. Derive the mathematical model of this system assuming small rotation angle 8. Link, moment. of inertia J L k₁ www m O k₂ www
4а. Show that the torque t = la, where I is the rotational inertia. Consider the pulley system shown in figure 4. Suppose the pulley is made up of a disc with mass Ma and a ring (hoop) with mass M, as shown in Figure 4a. Find the moment of inertia I, of the pulley through the center of mass. 4b. Find the angular acceleration a, of the pulley as a function of Ip, 0, M1, M2, µk. You may assume that there is no slipping between the pulley and the rope and the mass of the rope is negligibly small in comparison with the mass M1, and M2. The coefficient of friction between M2 and the incline is µk with M1> M2. 4c. Mr md MK outer ving (Mr) Central dise (Ma) RI axis at RAzti on X- Sedi on a pullag
A dancer is spinning at 72 rpm about an axis through her center with her arms outstretched, as shown in (Figure 1). From biomedical measurements, the typical distribution of mass in a human body is as follows: Part A Head: 7.0% Arms: 13% (for both) Trunk and legs: 80.0% Calculate moment of inertia about the dancer's spin axis. Express your answer with the appropriate units. Suppose the mass of the dancer is 64.5 kg, the diameter of her head is 16 cm, the width of her body is 24 length of her arms is 60 cm. cm, and the HÀ ? I = Value Units Submit Request Answer Figure 1 of 1 > Part B Calculate dancer's rotational kinetic energy. Express your answer with the appropriate units. ? K = Value Units Submit Request Answer
Gravitational acceleration g = 10 m/s? 1. A uniform thin rod of length Im and mass m,od = 20 Kg in the figure can rotate freely in the plane about an axis at 30 cm from one of its ends while the other end attached with a disk of radius 10 cm and mass maisk = 10 Kg. As the rod swings from the angle 30". a. Find the position center of mass. b. Calculate the moment of inertia for the composed system. c. What is the velocity of the disk while reaching an equilibrium point? 30 cm
Consider a cylinder of radius R = 0.6 m and radius of gyration k = 0.33 m rolling (without slipping) down an inclined plane. The plane makes an angle of ø = 10 deg with the horizontal plane. How long (in seconds) will it take for the center of cylinder to travel a distance of 1.3 m.
In the figure below there is one larger disc centred in O of radius 10 cm, a smaller disc centred in A of radius 3 cm, and an outer ring of neglectable thickness centred in O. The rod OA is fixed and cannot rotate, but the discs and the ring can rotate freely around their centres. B If the rotation speed of the inner larger disc centred in O is 2500 rpm, find the angular speed of the upper point B which is part of the outer ring, in rad/s.
A car is moving on a curved horizontal road of radius 100 m with a speed of 20 m/s. The rotating masses of the engine have an angular speed of 100 rad/s in clockwise direction when viewed from the front of the car The combined moment of inertia of the rotating masses is 10 kg-m².what is the magnitude of the gyroscopic moment in (N-m)?
find the equations of motion using the lagrange equations of motion. the car kas mass m and moment of inertia equal to Ic, exact dimensions needed to solve are on the picture. The bottom plate is moving to the left with the velocity v
A long uniform rod of length L= 50 cm and mass M = 250 g is pivoted about a horizontal, frictionless pin through one end. The rod is released from rest in vertical position. At the instant rod is horizontal as shown in the figure, find a) Find the its angular speed b) Find the magnitude of its angular acceleration c) Find the x and y components of the acceleration of its center of mass (The moment of inertia of the rod is I rod= 1/3 ML² with respect to pivot) Initial position L. Final position Pivot
a) An anemometer for measuring the wind speed consists of three thin, hemispherical shells of mass Meach and three connecting rods of mass mas shown in Figure Q1a. If the mass moment of inertia of the thin hemispherical shell about its centre of mass, axis GG' is given by 12 5 Ma? where a is the inner radius of the hemispherical shell. Find the mass moment of inertia of the anemometer about the axis AA'. Give your answer in terms of M, m, a and I. Consider the central rod as a thin rod. b) If the anemometer is rotating at 4 rev/sec. The system parameters are given as M=200g, m=90 g, a=40 mm and l=0.3m find the rotational kinetic energy and angular momentum. A' G