A wheel in the shape of a disk of radius R and mass M has moment of inertia about the centre BM R2 where ß < 1 is a positive constant. It is resting on a horizontal floor. A ball of mass m travels in a straight line with speed vi = v and hits the wheel and ricochets off vertically with speed V2 = . The radial line connecting the point where the ball hits the disk makes an angle 0 to the horizontal as shown. When the ball bounces off, the wheel starts to move along the floor. You can assume that the ball is a point mass and that the floor is frictionless. You are given cos 0 = and sin 0 = All your answers should be in terms of M, m, ß, R, v and dt(to be defined later) as necessary. V2 M

A wheel in the shape of a disk of radius R and mass M has moment of inertia about the centre BM R2 where ß < 1 is a positive constant. It is resting on a horizontal floor. A ball of mass m travels in a straight line with speed vi = v and hits the wheel and ricochets off vertically with speed V2 = . The radial line connecting the point where the ball hits the disk makes an angle 0 to the horizontal as shown. When the ball bounces off, the wheel starts to move along the floor. You can assume that the ball is a point mass and that the floor is frictionless. You are given cos 0 = and sin 0 = All your answers should be in terms of M, m, ß, R, v and dt(to be defined later) as necessary. V2 M

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

Two disks A and B, of mass m 1 kg each and of radius 10 cm, are placed on a horizontal table. The disk A is launched in translation with a speed of 10 m/s along the y axis, B is at rest. The coefficient of kinetic friction between the disks is 0.5. The line of impact is at an angle of 60° with the x-axis. The moment of inertia of each disk around its center of mass is I = 1₂ = 0.005 kg.m². The coefficient of restitution between the two disks is e=0.6. a) Determine the velocities of the centers of the two disks, just after the impact. b) Calculate the angular velocities of the disks, just after the impact. c) Calculate the energy loss during the impact.
Consider a slender rod AB with a length l and a mass m. The ends are connected to blocks of negligible mass sliding along horizontal and vertical tracks. If the rod is released with no initial velocity from a horizontal position as shown in Fig.A, determine its angular velocity after it has rotated through an angle of θ (see Fig B) using the conservation of energy method. (Hint: Moment of inertia of rod about G = (1/12)ml2 The kinetic energy of a rigid body in plane motion is
A massive sphere, with 10,0cm radius and moment of inertia I=4,00 x 10-3 kg-m² in relation to a straight line passing through the center of mass, rolls without sliding, descending a surface with an inclination of 30º in relation to the horizontal. In a certain initial position the total kinetic energy of the sphere is 17.5j . a Sketch the physical situation by identifying all the forces acting on the sphere in the initial position. (b) How much of this initial kinetic energy is due to rotation? (c)
A 256-lb block is released from rest when the spring is unstretched. The drum has a weight of 76 lb and a radius of gyration of kO = 0.9 ft about its center of mass O. The coefficient of stiffness of the spring is k=78 lb/ft. The radius of the drum are: rin=0.485ft and rout=0.82ft. Find the velocity of the block after it has descended d=4 feet.
5) In ice figure skating, a couple execute a “top” (see picture). The centre of mass of the woman (58 kg) is situated 1.3 m from the axis of rotation which is vertical and passes through the centre of mass of the man (85 kg). They are spinning at a constant angular velocity equal to 3.1415 rad/s and the man and woman have moments of inertia, about their own centres of mass, equal to 1.6 and 2.5 kg.m2 respectively. Then the woman grabs the neck of the man. At this point, her moment of inertia decreases to 1.4 kg.m2 and her body centre of gravity is 0.9 m from the axis of rotation. Determine the new angular velocity. Hints: This is a conservation of angular momentum problem, and needs the parallel axis theorem to determine moments of inertia about the axis of rotation. The skaters are moving as one body with one angular velocity, but they each have their own moments of inertia given relative to their own CoMs. For the man, that’s fine…the axis they’re rotating about passes through his…
A 7.5 kg disk A radius of 0.6 m initially rotating clockwise at 300 rev/min is engaged with an 8.5 kg disk B of radius 0.4 m initially rotating counter clockwise at 700 rev/min, where the moment of inertia of a disk is given as I=1/2mr^2. Determine their combined angular speed (in rpm) and direction after the meshing of the two disks.
A cable is wrapped around the spool’s center hub. The mass of the spool is m= 100 kg, the radius r1 = 0.4 m, r2 =0.6 m, and the radius of gyration is kG = 0.3 m. A horizontal force P = 10 N is applied to the cord. The spool is initially at rest and rolls without slipping. (2) The mass moment of inertia about point A _______(kg·m2)(two decimal places)
A uniform rod (mass = 1.8 kg) is 1.5 m long. The rod is pivoted about a horizontal, frictionless pin through one end. The rod is released from rest in a horizontal position. What is the angular speed of the rod (in rad/s) when the rod makes an angle of 23° with the horizontal?. The moment of inertia of the rod about this axis is given by (1/3)ML2.
A rotating shaft carries four unbalanced masses 20 kg, 16 kg, 18 kg and 14 kg at radii 55 mm, 65 mm, 75 mm and 65 mm respectively. The 2nd, 3rd and 4th masses revolve in planes 80 mm, 160 mm and 280 mm respectively measured from the plane of the first mass and are angularly located at 65°, 135° and 270° respectively measured clockwise from the first mass.The shaft is dynamically balanced by two masses, both located at 55 mm radii and revolving in planes mid-way between those of 1st and 2nd masses and midway between those of 3rd and 4th masses. Determine, balancing mass by drawing couple polygon and their respective angular position graphically.
A turbine rotor is found to be out of balance to the extent of 1.5 kg at 0.45 m radius in the plane AA and 2kg at 0.6 m radius in the plane BB, the relative angular positions being given in the end view. It is desired to balance these masses by a mass in each of the planes XX and YY at radii of 0.525m and 0.45m respectively. Determine the magnitude and positions of these masses and show their positions in an end view. (Answer: X, 1.42kg, 209.27 degrees from A; y, 2.12KG, 329.1 degrees from A)
A drum of mass Ma and radius a rotates freely withinitial angular velocity ωa0. A second drum with mass Mb and radiusb > a is mounted on the same axis and is at rest, although it is free torotate. A thin layer of sand with mass Ms is distributed on the innersurface of the smaller drum. At t = 0, small holes in the inner drumare opened. The sand starts to fly out at a constant rate λ = dm/dtand sticks to the outer drum. (a) Explain, in detail, why the angularvelocity of the inner drum will remain constant. (b) Determine theangular velocity of the outer drum ωb(t). Ignore the transit time ofthe sand
A flywheel is a mechanical device used to store rotational kinetic energy for later use. Consider a flywheel in the form of a uniform solid cylinder rotating around its axis, with moment of inertia I = 1/2 mr2. 1) Consider a scenario in which the flywheel described in part (a) (r1 = 0.55 m, mass m1 = 16 kg, v = 45 m/s at the rim) is spinning freely at its maximum speed, when a second flywheel of radius r2 = 2.8 m and mass m2 = 11 kg is coaxially dropped from rest onto it and sticks to it, so that they then rotate together as a single body. Calculate the energy, in joules, that is now stored in the wheel. 2) Return now to the flywheel of part (a), with mass m1, radius r1, and speed v at its rim. Imagine the flywheel delivers one third of its stored kinetic energy to car, initially at rest, leaving it with a speed vcar. Enter an expression for the mass of the car, in terms of the quantities defined here.