question (c), (d), (e), (f) please. Thanks.
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1 Consider a cylinder of mass M and radius a rolling down a half-cylinder of radius R as shown in...
question (c), (d), (e), (f) please. Thanks. 1 Consider a cylinder of mass M and radius...
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...
Consider a uniform disk of mass m, and radius R that is rolling with slipping. The surface has a ...
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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...
2. (35pts) Consider a disc with a mass m rolling down from the top of the...
2. (35pts) Consider a disc with a mass m rolling down from the top of the cylinder without slipping. The radius of the cylinder is R while the radius of the disc is a. Ø is the angle of rotation of the disc while 0 is the polar coordinate of the cylinder. This problem has DOF=1. However, please use 0 and Ø as generalized coordinates. To simplify the problem, you can use constant r = R + a. R a)...
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...
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...
Q3. For the system in Figure 3 where and θ2 are the rotational angles, and are the rotary inertias of the two disks with radius r and 2r, respectively, 2r (1) Find its total kinetic energy, total pot...
Q3. For the system in Figure 3 where and θ2 are the rotational angles, and are the rotary inertias of the two disks with radius r and 2r, respectively, 2r (1) Find its total kinetic energy, total potential energy and Lagrangian in terms of, and (2) Derive the equations of motion using Lagrangian equation method, (3) Put the equations of motion in matrix form, and (4) Calculate the natural frequencies and the associated mode shapes if m-30 g, 4-8 x...
A cylinder of mass M and radius R is rolling down an incline with angle theta....
A cylinder of mass M and radius R is rolling down an incline with angle theta. Find the acceleration of the cylinder as it rolls down the incline. Find the acceleration a and the tension T in the string of a yo-yo when it is released.
Bridging Problem: Oscillating and Rolling Two uniform, solid cylinders of radius R and total mass M...
Bridging Problem: Oscillating and Rolling Two uniform, solid cylinders of radius R and total mass M are connected along their common axis by a short, light rod and rest on a horizontal tabletop (Figure 1). A frictionless ring at the rod's center is attached to a spring of force constant k, the spring's other end is fixed. The cylinders are pulled to the left a distance I, stretching the spring, then released from rest. Due to friction between the tabletop...
6. (Bonus question.) A small uniform cylinder of radius R rolls without slipping along the inside...
6. (Bonus question.) A small uniform cylinder of radius R rolls without slipping along the inside of a large, fixed cylinder of radius r > R as shown in the figure above. mig (a) Use conservation of energy to show that the period of small oscillations (θ « 1) of the rolling cylinder about the equilibrium position O is equivalent to that of a simple pendulum whose length is (r-R). [Note that the rotation rate w of the cylinder is...
A sphere of radius ? is constrained to roll without slipping on the lower half of...
A sphere of radius ? is constrained to roll without slipping on the lower half of the inner surface of a hollow cylinder of inside radius R. Determine the Langrangian function, the equation of constraints, and Lagrange’s equation of motion. Find the frequency of small oscillations. please explain what/why you're doing what you're doing. thank you
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 ens...
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...
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...
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...
2. (35pts) Consider a disc with a mass m rolling down from the top of the cylinder without slipping. The radius of the cylinder is R while the radius of the disc is a. Ø is the angle of rotation of the disc while 0 is the polar coordinate of the cylinder. This problem has DOF=1. However, please use 0 and Ø as generalized coordinates. To simplify the problem, you can use constant r = R + a. R a)...
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...
Q3. For the system in Figure 3 where and θ2 are the rotational angles, and are the rotary inertias of the two disks with radius r and 2r, respectively, 2r (1) Find its total kinetic energy, total potential energy and Lagrangian in terms of, and (2) Derive the equations of motion using Lagrangian equation method, (3) Put the equations of motion in matrix form, and (4) Calculate the natural frequencies and the associated mode shapes if m-30 g, 4-8 x...
A cylinder of mass M and radius R is rolling down an incline with angle theta. Find the acceleration of the cylinder as it rolls down the incline. Find the acceleration a and the tension T in the string of a yo-yo when it is released.
Bridging Problem: Oscillating and Rolling Two uniform, solid cylinders of radius R and total mass M are connected along their common axis by a short, light rod and rest on a horizontal tabletop (Figure 1). A frictionless ring at the rod's center is attached to a spring of force constant k, the spring's other end is fixed. The cylinders are pulled to the left a distance I, stretching the spring, then released from rest. Due to friction between the tabletop...
6. (Bonus question.) A small uniform cylinder of radius R rolls without slipping along the inside of a large, fixed cylinder of radius r > R as shown in the figure above. mig (a) Use conservation of energy to show that the period of small oscillations (θ « 1) of the rolling cylinder about the equilibrium position O is equivalent to that of a simple pendulum whose length is (r-R). [Note that the rotation rate w of the cylinder is...
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...
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