A disk of mass M and radius R is on the horizontal table, and an external...
Problem 4 A uniform solid spherical ball of mass M and radius R rests on a horizontal surface. Assume a constant coefficient of friction (this means that the frictional force is equal to the normal force multiplied by u). The acceleration due to gravity is g. At time t 0, the bal is struck impulsively on center, causing it to go instantaneously from rest to initial rotation horizontal speed vo with a no (a) Find the horizontal speed, and the...
Consider a uniform disk of radius R and mass m sliding down an incline making an angle θ with respect to the horizontal. The coefficient of kinetic friction between the disk and the surface is μk. The torque due to friction causes the disk to rotate as it slides down the incline. a) Compute the linear acceleration of the disk as it slides down the incline. b) Compute the angular acceleration of the disk as it slides down the incline....
ANS: PLEASE USE LAGRANGIAN, THANK YOU, WILL UPVOTE GOOD ANSWER IMMEDIATELY Consider a uniform disk of mass m, and radius R that is rolling with slipping. The surface has a coefficient of kinetic friction a) Find the equations of motion. b) Next consider the same disk when it is rolling without slipping. Find the EOM using either x or θ. Hint: be careful with the generalized force for θ. If we label point P as the point on the disk...
1. (20 points) Two forces F and F, are exerted on a disk with radius R = .5m and a mass M 5kg uniformly distributed F = 30N is exerted upwards and applied a distance R to the right of the disk's center. F = 60N is cxerted downwards and applied a distance R/2 to the left of the disk's center, R/2 E a) What is the aceleration of the center of mass and the angular acceleration around the center...
81. A uniform disk with a mass of m and a radius of r rolls without slipping along a horizontal surface and ramp, as shown above. The disk has an initial velocity of v. What is the maximum height h to which the center of mass of the disk rises? u2 2g 3u (A) hU (B) h=- u2 (C) h-U 2g
The mass of the symmetrical wheel shown below is m = 4 kg and its radius of gyration about its center is kg = 0.25 m. The outer radius of the wheel is r2 = 0.4 m. The radius of the inner hub, where a cable is wrapped around it, is rı = 0.2 m. The wheel rolls without slipping. The force P, applied to the cable, is increased slowly according to the linear relation P = at, where P...
Problems 1. (30 points.) A uniform circular disk is rolling without slipping on a horizontal surface with an initial speed of 12 m/s. The disk then rolls without slipping up a ramp of height 3.0 m and length (along the ramp's surface) of 12.0 m. Coming to the end of the ramp, it shoots over the edge and ck to the ground. Calculate the magnitude of the angular velocity the disk will have about its center-of-mass when it hits the...
The circular disk has a 200 mm radius and mass of 25 kg. The radius of gyration k about the center of gravity is 175mm. The inner radius of the disk is 75 mm. A steady force of T=30 Newtons is applied cord wrapped around the inner radius. 3. angle 0 17° to a at an Find: The angular acceleration of the disk, a) b) The acceleration of the mass centre G The friction force F from the ground acting...
Q7 (15 points): A solid cylinder of mass 5 kg and radius R 0.15 m rolls without slipping on a horizontal surface and is accelerated to the right by a constant force F of magnitude 6 N that is applied at the cylinder by a massless rope as shown in the below figure. Find a) the magnitude of the acceleration of the center of mass of the cylinder, b) the magnitude of the angular acceleration of the cylinder about the...
Rolling Without Slipping & Conservation of Mechanical Energy 1. A caveman applies a horizontal force of 800 N at height of 0.1 m above the center of a large spherical boulder of mass 400 kg and radius of 0.5 m (treat as a sphere: lon-2/5 mr2). Assume the sphere starts from rest and rolls horizontally without slipping. a) Draw a free-body diagram and label all the forces at their point of contact. b) Write equations applying Newton's 2 nd law...