A solid disk with a mass of 40 kg and a radius of 0.6 m can rotate around an axis through its center, perpendicular to the disk surface. At time t = 0 s, the disk is not turning. It has a constant angular acceleration ↵ and by t = 20 s it has completed 500 complete turns. Calculate the angular acceleration ↵. Calculate the angular velocity ! at t = 20 s. Calculate the rotational kinetic energy at t...
The disk of radius r = 1.5 m rolls without slipping on the incline with angle 0 = 30°. Simultaneously, the small particle A moves along the slot located at distance d = 0.3 m from the center of the disk. At the instant shown, the disk has a constant clockwise angular speedw = 1 rad/s, and the particle is in position x = 0.4 m which is increasing at a constant rate į = 1.3 m/s. Determine the magnitude...
A string is wrapped around a uniform disk of mass M = 2.2 kg and radius R = 0.1 m. (Recall that the moment of inertia of a uniform disk is (1/2) MR2.) Attached to the disk are four low-mass rods of radius b = 0.13 m, each with a small mass m = 0.7 kg at the end. The device is initially at rest on a nearly frictionless surface. Then you pull the string with a constant force F...
A solid disk of mass m = 9.2 kg and radius R = 0.2 m is rotating with a constant angular velocity of w = 38 rad/s. A thin rectangular rod with mass m2 = 3.7 kg and length L = 2R = 0.4 m begins at rest above the disk and is dropped on the disk where it begins to spin with the disk. 1) What is the initial angular momentum of the rod and disk system? kg-m2/s Submit...
A disk with mass m = 8.8 kg and radius R = 0.36 m begins at rest and accelerates uniformly for t = 16.5 s, to a final angular speed of ω = 31 rad/s. 1) What is the change in rotational energy of the disk? 2) What is the tangential component of the acceleration of a point on the rim of the disk when the disk has accelerated to half its final angular speed? 3) What is the magnitude...
6. A disk with a mass M, a radius R, and a rotational inertia of I- MR is attached to a horizontal spring which has a spring constant of as shown in the diagram. When the spring is stretched by a distance x and then released from rest, the disk rolls without slipping while the spring is attached to the frictionless axle within the center of the disk (a) Calculate the maximum translational velocity of the disk in terms of...
6/105 The semicircular disk of mass m = 2 kg is mounted in the light hoop of radius r = 150 mm and released from rest in position (a). Determine the angular velocity ω of the hoop and the normal force N under the hoop as it passes position (b) after rotating through 180°. The hoop rolls without slipping. The answer is displayed, please SHOW ALL WORK leading up to the answer. Include steps 6/105 The semicircular disk of mass...
A disk with mass m = 8.6 kg and radius R = 0.35 m begins at rest and accelerates uniformly for t = 18.9 s, to a final angular speed of ω = 29 rad/s. (answer all parts of this question please, thank you so so much) 1) What is the angular acceleration of the disk? 2) What is the angular displacement over the 18.9 s? 3) What is the moment of inertia of the disk? 4) What is the...
A disk of m=5 kg and radius r=2 m starts from rest and rolls down a 20 degree incline from an initial height of 50 m. What is the linear velocity of the disk as it reaches the bottom of the incline? What is the rotational kinetic energy of the disk at the halfway point between the positions 1 and 2? If it takes 1.2 seconds for the disk to reach the bottom of the incline, find the magnitude of...
2.00 m 30 Given: A solid sphere of mass m 0.60 kg and radius r 0.20 m is released from rest at the top of the incline shown. For this system, the coefficient of dynamic (sliding) friction is Hdyn 0.3 and the coefficient of static friction is Hstatic -0.5 Find: (a) Assume that the sphere rolls without slipping down the incline. Under this assumption, what is the acceleration of the sphere parallel to the incline, and how long does it...