A mass m has a massless hook of length 2L attached to it. The end of...
A mass m has a massless hook of length 2L attached to it. The end of this hook is a massless sticky scoop. This system of mass and hook is initially at rest. Another mass m flies with speed v1 directly into this scoop, sticks, and the whole thing starts to move and rotate. Find expressions for the linear and rotational velocity of the combined object after the first mass is caught.
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A mass m has a massless hook of length 2L attached to it. The
end of...
An inextensible massless string of length 2l has mass mand m3 attached to the two ends...
An inextensible massless string of length 2l has mass mand m3 attached to the two ends A and B respectively. A particle of mass m2 is attached to the midpoint of the string at point C. Initially, the three particles are at the vertices of an equilateral triangle as shown in the figure below and the string is taut. Particle 2 is given an impulse J along the bisector of the angle ACB. It is known that the whole set...
A massless rod of length l has weights, each of mass m, attached to its ends....
A massless rod of length l has weights, each of mass m, attached to its ends. The rod is initially put in a horizontal position, and laid on an off-center fulcrum located at a distance b from the rod’s center. The rod will topple. a) Calculate the total gravitational torque on the rod directly, by adding the two torques. b) Verify that this gives the same result as would have been obtained by taking the entire gravitational force as acting...
A rod of mass M and length 2L is free to rotate in a vertical plane...
A rod of mass M and length 2L is free to rotate in a vertical plane about an axis through O, as shown in the figure. The axis is normal to the plane of the paper. Three mosses M, M, and 2M are attached to the rod as shown. With the rod in a horizontal position, the system is released from rest. (a) Find the net torque on the rod about the axis of rotation immediately after the system is...
AXis Two spheres of mass m are attached to a light rod of length 2L. The...
AXis Two spheres of mass m are attached to a light rod of length 2L. The rod is fixed at its center to a freely-rotating axis. The rod is horizontal when a small bird of mass 5m carefully lands on the right sphere. Express a answers in terms of m, L, and g (a) What is the net torque on the system the instant the bird lands (while the rod is still horizontal)? (b) Determine the angular acceleration of the...
A rigid rotor has two particles of mass m attached to the ends of a massless...
A rigid rotor has two particles of mass m attached to the ends of a massless rigid rod of length a. The rotor is free to rotate in three dimensions about the center of mass. This is a model for the rotational motion of a homonuclear diatomic molecule, a molecule with two identical nuclei. (An example is 16O2.) (a) By expressing the Hamiltonian in terms of the orbital angular momentum, show that the allowed energies of this rigid rotor are...
A cylinder of length L=0.4m and a mass M=2kg has one end pinned to the surface,...
A cylinder of length L=0.4m and a mass M=2kg has one end pinned to the surface, in a frictionless environment. When another point mass, of m=0.1kg and velocity 5 m/s, hits it right at the end the point mass sticks to the cylinder and they both rotate around the pin. a.) What is the final angular velocity after the collision? b.) What is the linear velocity of the point mass stuck on the end of the the cylinder?
2) A particle of mass m, is attached to a massless rod of length L which...
2) A particle of mass m, is attached to a massless rod of length L which is pivoted at O and is free to rotate in the vertical plane as shown below. A bead of mass my is free to slide along the smooth rod under the action of a spring of stiffness k and unstretched length Lo. (a) Choose a complete and independent set of generalized coordinates. (b) Derive the governing equations of motion. m2
The assembly shown in the figure below consists of a thin rod of length l = 23.9 cm and mass m = 1.20 kg with a solid ball of diameter d = 10.0 cm and mass M = 2.00 kg attached to its top.
The assembly shown in the figure below consists of a thin rod of length l = 23.9 cm and mass m = 1.20 kg with a solid ball of diameter d = 10.0 cm and mass M = 2.00 kg attached to its top. The assembly is free to pivot about a frictionless axle through the bottom of the rod. The assembly is initially vertical and at rest when it starts to rotate clockwise. (a) After the combination rotates through 90...
A bob of mass m is attached to a massless rigid rod of length L at...
A bob of mass m is attached to a massless rigid rod of length L at an angle, theta, which is in turn attached to a firctionless hinge. A constant force, F = Fî acts on the bob. If the system begins at rest at theta = pi/5, find (a) its kinematic energy when it reaches theta = pi/30 and (b) its angular momentum when it reaches theta = 0.
an 8kg flywheel of radius r is initially at rest. assume the radius of the gyration kG= 0.12m and the radius of the flywheel r = 0.125m. an object B also of mass 8 kg is attached to a cord that is wra...
an 8kg flywheel of radius r is
initially at rest. assume the radius of the gyration kG= 0.12m and
the radius of the flywheel r = 0.125m. an object B also of mass 8
kg is attached to a cord that is wrapped around a periphery of the
flywheel. the fly wheel starts to rotate clockwise with angular
velocity. the rotation is resisted by a constant frictional torque
mf in the bearing 1Nm. use the work energy principle to determine...
An inextensible massless string of length 2l has mass mand m3 attached to the two ends A and B respectively. A particle of mass m2 is attached to the midpoint of the string at point C. Initially, the three particles are at the vertices of an equilateral triangle as shown in the figure below and the string is taut. Particle 2 is given an impulse J along the bisector of the angle ACB. It is known that the whole set...
A rod of mass M and length 2L is free to rotate in a vertical plane about an axis through O, as shown in the figure. The axis is normal to the plane of the paper. Three mosses M, M, and 2M are attached to the rod as shown. With the rod in a horizontal position, the system is released from rest. (a) Find the net torque on the rod about the axis of rotation immediately after the system is...
AXis Two spheres of mass m are attached to a light rod of length 2L. The rod is fixed at its center to a freely-rotating axis. The rod is horizontal when a small bird of mass 5m carefully lands on the right sphere. Express a answers in terms of m, L, and g (a) What is the net torque on the system the instant the bird lands (while the rod is still horizontal)? (b) Determine the angular acceleration of the...
2) A particle of mass m, is attached to a massless rod of length L which is pivoted at O and is free to rotate in the vertical plane as shown below. A bead of mass my is free to slide along the smooth rod under the action of a spring of stiffness k and unstretched length Lo. (a) Choose a complete and independent set of generalized coordinates. (b) Derive the governing equations of motion. m2
an 8kg flywheel of radius r is
initially at rest. assume the radius of the gyration kG= 0.12m and
the radius of the flywheel r = 0.125m. an object B also of mass 8
kg is attached to a cord that is wrapped around a periphery of the
flywheel. the fly wheel starts to rotate clockwise with angular
velocity. the rotation is resisted by a constant frictional torque
mf in the bearing 1Nm. use the work energy principle to determine...
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