A turntable has a radius of 0.80 m and a moment of inertia of 2.0 kg m2. The turntable is rotating with an angular velocity of 1.5 rad/s about a vertical axis though its center on frictionless bearings. A very small 0.40-kg ball is projected horizontally toward the turntable axis with a velocity of 3.0 m/s. The ball is caught by a very small and very light cup-shaped mechanism on the rim of the turntable (see figure).
a) What is the angular velocity of the turntable just after the ball is caught?
b) What is percentage of the initial kinetic energy of the system that is lost during the capture of the ball?
(a)
(Angular momentum conservation)
(b)
percentage = 50.86%
A turntable has a radius of 0.80 m and a moment of inertia of 2.0 kg m2. The turntable is rotating with an angular velocity of 1.5 rad/s about a vertical axis though its center on frictionless bearings.
7) A turntable with moment of inertia IT = 0.042 kg m2 and radius R = 0.24 m is rotating with ω = 0.68 rad/s. A mouse of mass m = 0.053 kg is standing on the edge of the turntable. a) What are the total moment of inertia and the total angular momentum of this system? b) If the mouse walks towards the center of the turntable, does the angular velocity increase or decrease? Explain the answer conceptually. c)...
A turntable with a rotational inertia 0.215 kg middot m^2 is rotating at 3.35 rad/s. Suddenly, a disk with rotational inertia 0.106 kg times m^2 is dropped onto the turntable with its center on the rotation axis. Assuming no outside forces act, what's the common rotational velocity of the turntable and disk?
A 55.0-kg woman stands at the rim of a horizontal turntable having a moment of inertia of 540 kg · m2 and a radius of 2.00 m. The turntable is initially at rest and is free to rotate about a frictionless vertical axle through its center. The woman then starts walking around the rim clockwise (as viewed from above the system) at a constant speed of 1.50 m/s relative to the Earth. (a) In what direction does the turntable rotate?...
A 3.9-m-diameter merry-go-round is rotating freely with an angular velocity of 0.80 rad/s . Its total moment of inertia is 1350 kg⋅m2 . Four people standing on the ground, each of mass 68 kg , suddenly step onto the edge of the merry-go-round. What is the angular velocity of the merry-go-round now?
As seen from above, a playground carousel is rotating counterclockwise about its center on frictionless bearings. A person standing still on the ground grabs onto one of the bars on the carousel very close to its outer edge and climbs aboard. Thus, this person begins with an angular speed of zero and ends up with a nonzero angular speed, which means that he underwent a counterclockwise angular acceleration. The carousel has a radius of 1.56 m, an initial angular speed...
A flat horizontal disc of moment of inertia 2.2 kg m2 is rotating at 4.5 rad s-1 about a vertical axis through its centre. A 0.13 kg mass is dropped onto the disc, landing without slipping 1.4 m from the centre. Calculate the new angular velocity of the disc, in rad s-1 , to 2d.p.
A uniform disk has a mass of 3.7 kg and a radius of 0.40 m. The disk is mounted on frictionless bearings and is used as a turntable. The turntable is initially rotating at 30 rpm. A thin - walled hollow cylinder has the same mass and radius as the disk. It is released from rest, just above the turntable, and on the same vertical axis. The hollow cylinder slips on the turntable for 0.20 s until it acquires the...
A merry-go-round with moment of inertia 400 kg-m^2 and radius 2.0m is rotating with angular speed 0.50 rad/s in the clockwise direction about a fixed axis. A child of mass 40 kg runs tangentially to the merry-go-round with speed 3.0m/s and grabs onto the outside edge of the merry-go-round. a. What is the final angular velocity of the system (merry-go-round plus child)/ What is the final tangential speed of the child? b. What is the change in kinetic energy? c....
A 4.4-m-diameter merry-go-round is rotating freely with an angular velocity of 0.90 rad. Its total moment of inertia is 1360 kg⋅m2 . Four people standing on the ground, each of mass 62 kg , suddenly step onto the edge of the merry-go-round. A) What is the angular velocity of the merry-go-round now? B) What if the people were on it initially and then jumped off in a radial direction (relative to the merry-go-round)?
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 ??...