A metal disc spins with an angular velocity ω0 about its center. A second disc (initially...
A metal disc spins with an angular velocity ω0 about its center. A second disc (initially stationary) is dropped on top of the first disc. The second disc is made of the same material as the first but has only half the diameter (so its mass will also be smaller). (a) Show that the moment of inertia of the second disc is 1/16th the moment of inertia of the first. (b) State why the angular momentum of the system (the two discs) is conserved. (c) The discs stick and spin together with the same angular velocity. Find this final angular velocity in terms of ω0.
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A metal disc spins with an angular velocity ω0 about its center.
A second disc (initially...
A disc of moment of inertia 3.00 kgm2 is rotating with angular velocity 2.00 rad/s about...
A disc of moment of inertia 3.00 kgm2 is rotating with angular velocity 2.00 rad/s about an axis perpendicular to its plane and passing through its centre. Another disk (which is not rotating) of moment of inertia 5.00 kgm2 is gently placed over it. Finally, the two discs rotate with the same angular velocity around the common rotational axis. The new angular velocity of the combined disc (in rad/s) is ?
A cylinder with moment of inertia I1 rotates with angular velocity ω0 about a frictionless vertical axle.
A cylinder with moment of inertia I1 rotates with angular velocity ω0 about a frictionless vertical axle. A second cylinder, with moment of inertia I2, initially not rotating, drops onto the first cylinder (Fig. P8.55). Because the surfaces are
rough, the two eventually reach the same angular velocity,ω.Figure P8.55(a) Calculate ω. (Use I1
for I1, I2 for I2, and w0
for ω0 in yourequation.)(b) Show that energy is lost in this situation (Do this on
paper.Your instructor may ask you to turn in this work.), and...
The physics students wish to test the law of conservation of angular momentum perform a completely...
The physics students wish to test the law of conservation of angular momentum perform a completely inelastic collision between two discs. They attach disc 1 (from part 1) to the rotational sensor then give it a spin. After about 4 seconds, they drop disc 2 on top of disc 1. The whole process takes only ~10 seconds total. Use the rate of change of the single disc angular velocity and the duration of the collision to find a corrected value...
A disc (thin cylinder) of mass 0.1 kg and radius 0.41 m is rotating on a...
A disc (thin cylinder) of mass 0.1 kg and radius 0.41 m is rotating on a frictionless axle at a constant rate of 74 RPM. What a the angular velocity and angular momentum of the disc? A second disc of 0.05 kg and 0.18 m is dropped down the axle on top. The two then rotate together. What is the final angular velocity and RPM of the system of discs?
A person spins with their arms extended at an angular velocity of 4 radians/second. When they...
A person spins with their arms extended at an angular velocity of 4 radians/second. When they bring their arms in, their angular velocity becomes 9 radians/second. Their moment of inertia with arms extended was I. What is the skater's moment of inertia with her arms drawn in?
9. A disc is rotating about a axis through the center at a constant angular velocity...
9. A disc is rotating about a axis through the center at a constant angular velocity oo. Two ants of equal mass suddenly drop onto the edge the disc and gets stuck to the rotating disc. Does the Moment of Inertia of the system increase or decrease? Explain a. b. Does the angular velocity increase or decrease? Explain 01 c. Now suppose the two ants start moving toward the center at a constant speed. i.Does the moment of inertia increase...
A disk with moment of inertia 9.15 × 10−3 kg∙m^2 initially rotates about its center at...
A disk with moment of inertia 9.15 × 10−3 kg∙m^2 initially rotates about its center at angular velocity 5.32 rad/s. A non-rotating ring with moment of inertia 4.86 × 10−3 kg∙m^2 right above the disk’s center is suddenly dropped onto the disk. Finally, the two objects rotate at the same angular velocity ?? about the same axis. There is no external torque acting on the system during the collision. Please compute the system’s quantities below. 1. Initial angular momentum ??...
To understand how to use conservation of angular momentum to solve problems involving collisions of rotating...
To understand how to use conservation of angular momentum to solve problems involving collisions of rotating bodies. Consider a turntable to be a circular disk of moment of inertia I_t rotating at a constant angular velocity omega_i around an axis through the center and perpendicular to the plane of the disk (the disk's "primary axis of symmetry"). The axis of the disk is vertical and the disk is supported by frictionless bearings. The motor of the turntable is off, so...
(3) A disk with moment of inertia 9.15 × 10−3 kg∙m 2 initially rotates about its...
(3) A disk with moment of inertia 9.15 × 10−3 kg∙m 2 initially rotates about its center at angular velocity 5.32 rad/s. A non-rotating ring with moment of inertia 4.86 × 10−3 kg∙m 2 right above the disk’s center is suddenly dropped onto the disk. Finally, the two objects rotate at the same angular velocity ?? about the same axis. There is no external torque acting on the system during the collision. Please compute the system’s quantities below. 1. Initial...
To understand how to use conservation of angular momentum to solve problems involving collisions of rotating bodies. (...
To understand how to use conservation of angular momentum to solve problems involving collisions of rotating bodies. (Figure 1) Consider a turntable to be a circular disk of moment of inertia It rotating at a constant angular velocity ωi around an axis through the center and perpendicular to the plane of the disk (the disk's "primary axis of symmetry"). The axis of the disk is vertical and the disk is supported by frictionless bearings. The motor of the turntable is...
A cylinder with moment of inertia I1 rotates with angular velocity ω0 about a frictionless vertical axle. A second cylinder, with moment of inertia I2, initially not rotating, drops onto the first cylinder (Fig. P8.55). Because the surfaces are
rough, the two eventually reach the same angular velocity,ω.Figure P8.55(a) Calculate ω. (Use I1
for I1, I2 for I2, and w0
for ω0 in yourequation.)(b) Show that energy is lost in this situation (Do this on
paper.Your instructor may ask you to turn in this work.), and...
9. A disc is rotating about a axis through the center at a constant angular velocity oo. Two ants of equal mass suddenly drop onto the edge the disc and gets stuck to the rotating disc. Does the Moment of Inertia of the system increase or decrease? Explain a. b. Does the angular velocity increase or decrease? Explain 01 c. Now suppose the two ants start moving toward the center at a constant speed. i.Does the moment of inertia increase...
To understand how to use conservation of angular momentum to solve problems involving collisions of rotating bodies. Consider a turntable to be a circular disk of moment of inertia I_t rotating at a constant angular velocity omega_i around an axis through the center and perpendicular to the plane of the disk (the disk's "primary axis of symmetry"). The axis of the disk is vertical and the disk is supported by frictionless bearings. The motor of the turntable is off, so...
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