Figure 8.16 shows a centrifugal regulator. The mass M is free to move in the vertical direction. The mass of the arms of leght l and the axis of the regulator can be neglected. The regulator rotates with a constant angular speed w. Calculate the distance z of the mass M from its lowest possible position and the frequency of small oscillations of z around equilibrium state,
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Figure 8.16 shows a centrifugal regulator. The mass M is free to move in the vertical...
A bead of mass M is able to move without friction along a stationary horizontal rod...
A bead of mass M is able to move without friction along a stationary horizontal rod (directed along the x axis). In addition, a second body of mass m is attached to the first bead and suspended below it via a massless rod of length a. This second mass and rod form a pendulum that is able to swing in the xy-plane (where y is the vertical axis). (a) Obtain the Lagrangian for the system of two masses. (b) Assuming...
4. A particle of mass m and charge q is constrained to move along a straight...
4. A particle of mass m and charge q is constrained to move along a straight line between two point charges of equal charge Q separated by distance 2L. The sign of all three charges is the same so that the charge q is repelled by the other two particles. (a) (5 points) What is equilibrium position of charge q? Use the symmetry of the system. Is the equilibrium stable or unstable? (b) (5 points) Chose the origin of your...
The figure shows a rigid assembly of a thin hoop (of mass m = 0.27 kg...
The figure shows a rigid
assembly of a thin hoop (of mass m = 0.27 kg and radius R = 0.17 m)
and a thin radial rod (of length L = 2R and also of mass m = 0.27
kg). The assembly is upright, but we nudge it so that it rotates
around a horizontal axis in the plane of the rod and hoop, through
the lower end of the rod. Assuming that the energy given to the
assembly in...
A bead of mass m slides frictionlessly on a circle of wire with radius R. The...
A bead of mass m slides frictionlessly on a circle of wire with radius R. The circle stands up in a vertical plane and rotates about the z-axis with constant angular velocity . Write down the Lagrangian. Find the equations of motion. For an angular velocity greater than some critical angular velocity , the bead will experience small oscillations about some stable equilibrium point . Find and (). We were unable to transcribe this imageWe were unable to transcribe this...
The figure shows a rigid structure consisting of a circular hoop of radius R and mass...
The figure shows a rigid structure consisting of a circular hoop of radius R and mass m, and a square made of four thin bars, each of length R and mass m. The rigid structure rotates at a constant speed about a vertical axis, with a period of rotation of 4.3 s. If R = 1.1m and m = 1.8 kg, calculate the angular momentum about that axis.
The figure shows a rigid structure consisting of a circular hoop of radius R and mass...
The figure shows a rigid structure consisting of a circular hoop of radius R and mass m, and a square made of four thin bars, each of length R and mass m. The rigid structure rotates at a constant speed about a vertical axis, with a period of rotation of 3.5 s. If R = 1.2 m and m = 3.3 kg, calculate the angular momentum about that axis.
The figure shows a rigid structure consisting of a circular hoop of radius R and mass...
The figure shows a rigid structure consisting of a circular hoop of radius R and mass m, and a square made of four thin bars, each of length Rand mass m. The rigid structure rotates at a constant speed about a vertical axis, with a period of rotation of 3.5 s. If R = 1.2 m and m = 3.3 kg, calculate the angular momentum about that axis. Rotation axis Number Units
The figure shows a rigid structure consisting of a circular hoop of radius R and mass...
The figure shows a rigid structure consisting of a circular hoop of radius R and mass m, and a square made of four thin bars, each of length Rand mass m. The rigid structure rotates at a constant speed about a vertical axis, with a period of rotation of 2.1 s. If R=0.9 m and m-4.0 kg, calculate the angular momentum about that axis. Number i Units
Q3-(25 pts) A small bead of mass m can move on a fixed horizontal wire without...
Q3-(25 pts) A small bead of mass m can move on a fixed horizontal wire without friction as in the figure. The bead is connected to an ideal spring of spring constant k, and the other end of the spring is connected to a fixed point at a perpendicular distance d from the wire. Unstretched length of the spring is very small, and can be taken to be zero. a) What is the period of oscillations of the bead around...
The figure shows a rigid structure consisting of a circular hoop of radius R and mass...
The figure shows a rigid structure consisting of a circular hoop of radius R and mass m1 and a square made of four thin bars, each of length R and mass m. The rigid structure rotates at a constant speed about a vertical axis, with a period of rotation of s. If R = m and m = kg, calculate the angular momentum about that axis. At the instant of the figure, a kg particle P has a position vector...
A bead of mass M is able to move without friction along a stationary horizontal rod (directed along the x axis). In addition, a second body of mass m is attached to the first bead and suspended below it via a massless rod of length a. This second mass and rod form a pendulum that is able to swing in the xy-plane (where y is the vertical axis). (a) Obtain the Lagrangian for the system of two masses. (b) Assuming...
4. A particle of mass m and charge q is constrained to move along a straight line between two point charges of equal charge Q separated by distance 2L. The sign of all three charges is the same so that the charge q is repelled by the other two particles. (a) (5 points) What is equilibrium position of charge q? Use the symmetry of the system. Is the equilibrium stable or unstable? (b) (5 points) Chose the origin of your...
The figure shows a rigid
assembly of a thin hoop (of mass m = 0.27 kg and radius R = 0.17 m)
and a thin radial rod (of length L = 2R and also of mass m = 0.27
kg). The assembly is upright, but we nudge it so that it rotates
around a horizontal axis in the plane of the rod and hoop, through
the lower end of the rod. Assuming that the energy given to the
assembly in...
The figure shows a rigid structure consisting of a circular hoop of radius R and mass m, and a square made of four thin bars, each of length R and mass m. The rigid structure rotates at a constant speed about a vertical axis, with a period of rotation of 4.3 s. If R = 1.1m and m = 1.8 kg, calculate the angular momentum about that axis.
The figure shows a rigid structure consisting of a circular hoop of radius R and mass m, and a square made of four thin bars, each of length Rand mass m. The rigid structure rotates at a constant speed about a vertical axis, with a period of rotation of 3.5 s. If R = 1.2 m and m = 3.3 kg, calculate the angular momentum about that axis. Rotation axis Number Units
The figure shows a rigid structure consisting of a circular hoop of radius R and mass m, and a square made of four thin bars, each of length Rand mass m. The rigid structure rotates at a constant speed about a vertical axis, with a period of rotation of 2.1 s. If R=0.9 m and m-4.0 kg, calculate the angular momentum about that axis. Number i Units
Q3-(25 pts) A small bead of mass m can move on a fixed horizontal wire without friction as in the figure. The bead is connected to an ideal spring of spring constant k, and the other end of the spring is connected to a fixed point at a perpendicular distance d from the wire. Unstretched length of the spring is very small, and can be taken to be zero. a) What is the period of oscillations of the bead around...
The figure shows a rigid structure consisting of a circular hoop of radius R and mass m1 and a square made of four thin bars, each of length R and mass m. The rigid structure rotates at a constant speed about a vertical axis, with a period of rotation of s. If R = m and m = kg, calculate the angular momentum about that axis. At the instant of the figure, a kg particle P has a position vector...
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