The Figure below shows a homogeneous cylinder of radius R and mass m. Assuming that the...
1 Q2. Figure 2 shows a system in which mass m is connected with a cylinder of mass m2 and moment of inertia Jo through a horizontal spring k. The cylinder is m1 rolling on the rough surface without slipping. (1) Find its total kinetic energy, total potential energy TN and Lagrangian, Figure 2 (2) Derive the equations of motion using Lagrangian equation method, and (3) Calculate its natural frequencies 1 Q2. Figure 2 shows a system in which mass...
A uniform disk of radius r and mass md rolls without slipping on a cylindrical surface and is attached to a uniform slender bar AB of mass mb. The bar is attached to a spring of constant K and can rotate freely in the vertical plane about point A as shown in the figure . If the bar AB is displaced by small angle 0 and released, determine The energy of the system in terms of theta and theta '....
A non-uniform cylinder with mass M and radius R rolls without sliding across the floor. If it's mass was 2 kg and its radius 32 cm, and it was rolling at an angular speed of 13 rad/sec, how far up a hill can the cylinder roll without slipping?
Figure shows a solid cylinder of mass M=0.45 kg attached to a horizontal spring (k = 5.00 N/m) just slides on a frictionless surface. roooooo by 0.32 m, the cylinder's center of mass (COM) executes simple harmonic 1. Obtain the equation for the time period of the oscillation using Newton's second law of motion. The 2. Calculate the speed of the COM when it passes through the equilibrium. Show your work. (3 points) 3. If instead the surface is rough,...
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...
2. The homogeneous cylinder has a mass m and a radius R. It is placed on the cart and restrained by the cord. The coefficient of friction between the cylinder and the cart is Hs. Determine the largest acceleration a of the cart for which the cylinder does not slide. Solution: a = 24sg Cord
A non-uniform density cylinder has a radius R=6m. The rotational inertia of this cylinder can be taken to be I=βMR2, where β is unknown and M is the mass of the cylinder. The cylinder is initially rotating with angular velocity ω0= 1.00rad/s, and is placed on a rough horizontal surface. The speed of the center of mass (CM) of the cylinder, as it is placed on the surface, is 0. The cylinder at first rolls and slips. Just as it...
question (c), (d), (e), (f) please. Thanks. 1 Consider a cylinder of mass M and radius a rolling down a half-cylinder of radius R as shown in the diagram (a) Construct two equations for the constraints: i rolling without slipping (using the two angles and θ), and ii) staying in contact (using a, R and the distance between the axes of the cylinders r). (b) Construct the Lagrangian of the system in terms of θ1, θ2 and r and two...
4) Figures 4A (side view) and 4B (overhead view) illustrates a uniform solid cylinder having mass M and radius R. The cylinder is positioned on a horizontal floor having sufficient friction to ensure that the cylinder can roll without slipping. The cylinder includes a mass-less yoke that is fixed to the symmetric axis of the cylinder and acts as a rolling friction-less pivot for the cylinder. An ideal spring having spring constant K is attached to the yoke at one...
Find the angular velocity w3 at instant s1=0.2m KEl6. Figure shows a mechanism. Body 5 is assumed to be homogeneous circular cylinder, and mass of the pulley 4 is uniformly distributed over its rim. The coefficient of sliding friction between bodies and the plane is f 0.1. The coefficient of stiffness of a spring is e. A force Fapplied to the mechanism depends on the displacement si of the body 1. The mechanism starts motion from rest, and at the...