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Problem 6: A small mass m on a string is rotating without friction in a circle....
Object rotating on a string of changing length. A small mass m attached to the end...
Object rotating on a string of changing length. A small mass m attached to the end of a string revolves in a circle on a friction-less tabletop. The other end of the string passes through a hole in the table. Initially the mass revolves with a speed 2.4 m/s in a circle of radius 0.80 m. The string is then pulled slowly through the hole so that the radius i reduced to 0.48 m. The final speed is 4.0 m/s...
A bead of mass m slides without friction along a rotating wire in the shape of...
A bead of mass m slides without friction along a rotating wire in the shape of a parabola with zar2, as shown below. The wire is rotating around the z-axis with constant angular velocity w z=ar2 (a) (0.5 point) Determine the Lagrangian for the system in terms of the coordinate r b) (1 point) Apply the Lagrange Equations to obtain the equation of motion. You (c) (0.5 points) Suppose that the bead is moving in a perfect circle of radius...
A small coin (mass m) is placed on a disc that is rotating at a constant...
A small coin (mass m) is placed on a disc that is rotating at a constant angular speed ω. You know that the coefficient of static friction between the coin and the disc is μ. Determine the largest distance r from the axis of rotation that the coin can be placed so that it will not fly off the rotating disc. Reflection suggestion: Does the largest distance get bigger or smaller if you increase ω?
A small mass M attached to a string slides in a circle (x) on a frictionless...
A small mass M attached to a string slides in a circle (x) on a
frictionless horizontal table, with the force F
providing the necessary tension (see figure). The force is then
increased slowly and then maintained constant when M travels around
in circle (y). The radius of circle (x) is twice the radius of
circle (y).
Answer can be true,false,less than, greater than, equal to
(if you could leave an explanation that would be great!)
M's angular velocity at...
A small mass M attached to a string slides in a circle (x) on a frictionless...
A small mass M attached to a string slides in a circle (x) on a frictionless horizontal table, with the force F providing the necessary tension (see figure). The force is then increased slowly and then maintained constant when M travels around in circle (y). The radius of circle (x) is twice the radius of circle (y) X M's angular momentum at y is .... that at x M's angular velocity at y is four times that at x M's...
A small ball of mass m is tied to a string and set rotating with negligible...
A small ball of mass m is tied to a string and set rotating with negligible friction in a vertical circle of radius R with earth's gravity g acting. (a) What is the speed of the ball at the top of the circle so that the tension in the string vanishes there? (b) Given this, what is the speed of the ball at the bottom of the circle, and (c) what is the tension in the string at the bottom...
A small coin (mass m) is placed on a disc that is rotating at a constant...
A small coin (mass m) is placed on a disc that is rotating at a constant angular speed ω. You know that the coefficient of static friction between the coin and the disc is μ. Determine the largest distance r from the axis of rotation that the coin can be placed so that it will not fly off the rotating disc.
1. A small bead is free to slide without friction on a rotating wire. The angular...
1. A small bead is free to slide without friction on a rotating wire. The angular speed of the wire is w. In the coordinate system that rotates with the wire, there will be fictitious Coriolis and centrifugal forces, in addition to the real normal force the wire exerts on the bead. Working in this rotating coordinate system, (a) Draw the force diagram, including the fictitious forces. Write down the F=ma equations for the directions parallel and perpendicular to the...
Suppose you swing a ball of mass m in a vertical circle on a string of...
Suppose you swing a ball of mass m in a vertical circle on a string of length L. As you probably know from experience, there is a minimum angular velocity ωmin you must maintain if you want the ball to complete the full circle without the string going slack at the top. Find an expression for ωmin in terms of g and L . Evaluate ωmin in rpm for a 65 g ball tied to a 1.4-m-long string.
A plastic disk initially rotates freely and without friction on an icy surface, as shown in...
A plastic disk initially rotates freely and without friction on an icy surface, as shown in the figure. The disk completes 1.0 revolution every 0.75 seconds., The disk has a radius 0.035 m, a thickness o 0,0070 m, and a mass of 0.15 k seolution esery eled Bool Square face is 0.060 m by 0.060 m. 0.012 m rotating plastic icy surface (a) Calculate the initial angular velocity of the plastic disk in units of radians per second. (b) Calculate...
A bead of mass m slides without friction along a rotating wire in the shape of a parabola with zar2, as shown below. The wire is rotating around the z-axis with constant angular velocity w z=ar2 (a) (0.5 point) Determine the Lagrangian for the system in terms of the coordinate r b) (1 point) Apply the Lagrange Equations to obtain the equation of motion. You (c) (0.5 points) Suppose that the bead is moving in a perfect circle of radius...
A small mass M attached to a string slides in a circle (x) on a
frictionless horizontal table, with the force F
providing the necessary tension (see figure). The force is then
increased slowly and then maintained constant when M travels around
in circle (y). The radius of circle (x) is twice the radius of
circle (y).
Answer can be true,false,less than, greater than, equal to
(if you could leave an explanation that would be great!)
M's angular velocity at...
A small mass M attached to a string slides in a circle (x) on a frictionless horizontal table, with the force F providing the necessary tension (see figure). The force is then increased slowly and then maintained constant when M travels around in circle (y). The radius of circle (x) is twice the radius of circle (y) X M's angular momentum at y is .... that at x M's angular velocity at y is four times that at x M's...
A small ball of mass m is tied to a string and set rotating with negligible friction in a vertical circle of radius R with earth's gravity g acting. (a) What is the speed of the ball at the top of the circle so that the tension in the string vanishes there? (b) Given this, what is the speed of the ball at the bottom of the circle, and (c) what is the tension in the string at the bottom...
1. A small bead is free to slide without friction on a rotating wire. The angular speed of the wire is w. In the coordinate system that rotates with the wire, there will be fictitious Coriolis and centrifugal forces, in addition to the real normal force the wire exerts on the bead. Working in this rotating coordinate system, (a) Draw the force diagram, including the fictitious forces. Write down the F=ma equations for the directions parallel and perpendicular to the...
A plastic disk initially rotates freely and without friction on an icy surface, as shown in the figure. The disk completes 1.0 revolution every 0.75 seconds., The disk has a radius 0.035 m, a thickness o 0,0070 m, and a mass of 0.15 k seolution esery eled Bool Square face is 0.060 m by 0.060 m. 0.012 m rotating plastic icy surface (a) Calculate the initial angular velocity of the plastic disk in units of radians per second. (b) Calculate...
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