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here in kinetic energy i used v = sw relation.
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2. Two equal masses are attached to a massless hoop of radius R that is free to rotate about its ...
Problem 5 (15 points) A small bead can slide without friction on a circular hoop that...
Problem 5 (15 points) A small bead can slide without friction on a circular hoop that is a vertical plane and has a radius of 0.100 m. The hoop rotates at a constant rate of 4.00 rev/sec (recall 1 rev = 2π rad) about a vertical diameter as shown in the figure below (a) Find the angle β at which the bead is in vertical equilibrium. (It has a radial acceleration toward the axis.) (b) Is it possible for the...
Two equal masses, m, are joined by a massless string of length L that passes through...
Two equal masses, m, are joined by a massless string of length L
that passes through a hole in a frictionless horizontal table.
First mass slides on table while the second hangs below the table
and moves up and down in a vertical line.
a.) Assuming the string remains taut, write down the Lagrangian
for the system in terms of the polar coordinates
of the mass on the table.
b.) Find the two Lagrangian equations of motion and interpret
the...
A constant-density cylinder of mass 0.5 kg and radius 4 cm can rotate freely about an...
A constant-density cylinder of mass 0.5 kg and radius 4 cm can rotate freely about an axis through its center. It has thread wound around an attached axle of radius 0.5 cm that also runs through its center (Fig. as shown) The thread is attached to a mass of 1 kg, which slides down an inclined plane of angle ф-300 with an acceleration of 0.1 m/s. a) Draw a free body diagram of the system by PROBLEM 4: (12pts) R....
A vertical axis is free to rotate. A massless, horizontal rod is attached to the axis...
A vertical axis is free to rotate. A massless, horizontal rod is attached to the axis as shown. There are two small objects attached to the rod. One of the objects has mass m1 and is fixed At the end of the rod. The other. With mass m2, starts right, at the point where the rod is attached to the axle. The axle is given an angular velocity w0. at n time defined to be t = 0 the object...
A massless rod with length L is attached to two springs at its two masses (both...
A massless rod with length L is
attached to two springs at its two masses (both m) at its two ends.
The masses are connected to springs. The springs can move in the
horizontal and vertical directions as shown in the figure and they
both have a stiffness k. Note that gravity acts. Assume the springs
are un-stretched when the rod is vertical. Find the equation of
motion for the system using 1. Newton’s second law 2. Conservation
of energy....
A stick of length 1.5 m and mass 8.0 kg is free to rotate about a...
A stick of length 1.5 m and mass 8.0 kg is free to rotate about a horizontal axis through the center. Small bodies of masses 7.0 and 4.0 kg are attached to its two ends. The stick is released from the horizontal position. What is the angular velocity of the stick (in rad/s) when it swings through the vertical? (Enter the magnitude.)
A rigid, massless rod has three particles with equal masses attached to it as shown in Figure P8.59.
A rigid, massless rod has three particles with equal masses attached to it as shown in Figure P8.59. The rod is free to rotate in a vertical plane about a friction-less axle perpendicular to the rod through the point Pand is released from rest in the horizontal position at t - 0. Assuming m and d are known, find (a) the moment of inertia of the system (rod plus particles) about the pivot, (b) the torque acting on the system...
A stick of length 1.5 m and mass 9.0 kg is free to rotate about a...
A stick of length 1.5 m and mass 9.0 kg is free to rotate about
a horizontal axis through the center. Small bodies of masses 8.0
and 2.0 kg are attached to its two ends (see the following figure).
The stick is released from the horizontal position. What is the
angular velocity of the stick (in rad/s) when it swings through the
vertical? (Enter the magnitude.)
3. 25 points A uniform hoop of mass M and radius r has a uniform rod...
3. 25 points A uniform hoop of mass M and radius r has a uniform rod of mass m and length r welded to it as illustrated. a) Given that the rod is at an angle θ from the horizontal, and that the hoop is rotating at a rate ω and rolling on the floor without slipping, what is the total Kinetic Energy, and total Potential Energy (use the height of the center of the hoop as your datum)? Hints:...
A cylinder of radius R has the y axis as its central axis, and therefore appears...
A cylinder of radius R has the y axis as its central axis, and therefore appears as a circle in the diagram below. The cylinder does not move. A massless string of total length b (greater than TR) is attached to the cylinder as shown in the diagram. A point mass m is attached to the lower end of the string. The motion is in the xz plane. The point P is defined so that the string above P is...
Problem 5 (15 points) A small bead can slide without friction on a circular hoop that is a vertical plane and has a radius of 0.100 m. The hoop rotates at a constant rate of 4.00 rev/sec (recall 1 rev = 2π rad) about a vertical diameter as shown in the figure below (a) Find the angle β at which the bead is in vertical equilibrium. (It has a radial acceleration toward the axis.) (b) Is it possible for the...
Two equal masses, m, are joined by a massless string of length L
that passes through a hole in a frictionless horizontal table.
First mass slides on table while the second hangs below the table
and moves up and down in a vertical line.
a.) Assuming the string remains taut, write down the Lagrangian
for the system in terms of the polar coordinates
of the mass on the table.
b.) Find the two Lagrangian equations of motion and interpret
the...
A constant-density cylinder of mass 0.5 kg and radius 4 cm can rotate freely about an axis through its center. It has thread wound around an attached axle of radius 0.5 cm that also runs through its center (Fig. as shown) The thread is attached to a mass of 1 kg, which slides down an inclined plane of angle ф-300 with an acceleration of 0.1 m/s. a) Draw a free body diagram of the system by PROBLEM 4: (12pts) R....
A vertical axis is free to rotate. A massless, horizontal rod is attached to the axis as shown. There are two small objects attached to the rod. One of the objects has mass m1 and is fixed At the end of the rod. The other. With mass m2, starts right, at the point where the rod is attached to the axle. The axle is given an angular velocity w0. at n time defined to be t = 0 the object...
A massless rod with length L is
attached to two springs at its two masses (both m) at its two ends.
The masses are connected to springs. The springs can move in the
horizontal and vertical directions as shown in the figure and they
both have a stiffness k. Note that gravity acts. Assume the springs
are un-stretched when the rod is vertical. Find the equation of
motion for the system using 1. Newton’s second law 2. Conservation
of energy....
A stick of length 1.5 m and mass 9.0 kg is free to rotate about
a horizontal axis through the center. Small bodies of masses 8.0
and 2.0 kg are attached to its two ends (see the following figure).
The stick is released from the horizontal position. What is the
angular velocity of the stick (in rad/s) when it swings through the
vertical? (Enter the magnitude.)
3. 25 points A uniform hoop of mass M and radius r has a uniform rod of mass m and length r welded to it as illustrated. a) Given that the rod is at an angle θ from the horizontal, and that the hoop is rotating at a rate ω and rolling on the floor without slipping, what is the total Kinetic Energy, and total Potential Energy (use the height of the center of the hoop as your datum)? Hints:...
A cylinder of radius R has the y axis as its central axis, and therefore appears as a circle in the diagram below. The cylinder does not move. A massless string of total length b (greater than TR) is attached to the cylinder as shown in the diagram. A point mass m is attached to the lower end of the string. The motion is in the xz plane. The point P is defined so that the string above P is...
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