A ring (mass 4 M, radius 1 R) rotates in a CCW direction with an initial angular speed 2 ω. A disk (mass 4 M, radius 1 R) rotates in a CW direction with initial angular speed 4 ω. The ring and disk "collide" and eventually rotate together. Assume that positive angular momentum and angular velocity values correspond to rotation in the CCW direction.
1. What is the initial angular momentum Li of the
ring+disk system? Write your answer in terms of
MR2ω.
2. What is the final angular velocity ωf of the
ring+disk system? Write your answer in terms of ω.
A ring (mass 4 M, radius 1 R) rotates in a CCW direction with an initial...
A ring of mass 2 M and radius 1 R rotates in a CCW direction with initial angular speed 2 ω. A disk of mass 4 M and radius 1 R rotates in a CW direction with initial angular speed 4 ω. The ring and disk "collide" and eventually rotate together. Assume that positive angular momentum and angular velocity values correspond to rotation in the CCW direction. What are the moments of inertia for the ring and disk? Write your...
A ring (4 kg, r = 2 m) rotates in a CW direction with initial angular velocity 20 s-1. A disk (8 kg, r = 2 m) rotates in a CCW direction with initial angular velocity 60 s-1. The ring and disk "collide" and eventually rotate together. Assume that positive angular momentum and angular velocity values correspond to rotation in the CCW direction. What is the initial angular momentum Li of the ring+disk system? What is the final angular velocity...
Consider a cylindrical turntable whose mass is M and radius is R, turning with an initial angular speed ω1. (a) A parakeet of mass m, after hovering in flight above the outer edge of the turntable, gently lands on it and stays in one place on it, as shown below. What is the angular speed of the turntable after the parakeet lands? (Use any variable or symbol stated above as necessary.) ωf = (b) Becoming dizzy, the parakeet jumps off...
of mass m and radius R is freely rotating at angular velocityw,spinning clockwise The moment of inertia of a disk is ImR2.) While it is rotating, someone when seen from above. ( ps a thin ring of mass m and also of radius R on top of it. When the ring lands, it is initially ot otating, but friction quickly causes it to rotate along with the disk, but the rotation of the disk slows down. a) What principle of...
A disk of mass M and radius R is rotating with an angular velocity ω. A rod also of mass M but length 2R is initially not rotating. It is dropped vertically onto the rotating disk. After the collision, the disk and rod rotate together with an angular velocity of? What fraction of the initial kinetic energy was lost in the collision?
1a. A cockroach of mass m lies on the rim of a uniform disk of mass 9.00 m that can rotate freely about its center like a merry-go-round. Initially the cockroach and disk rotate together with an angular velocity of 0.456 rad/s. Then the cockroach walks halfway to the center of the disk. (a) What then is the angular velocity of the cockroach-disk system? (b) What is the ratio K/K0 of the new kinetic energy of the system to its...
A solid disk of mass m = 9.2 kg and radius R = 0.2 m is rotating with a constant angular velocity of w = 38 rad/s. A thin rectangular rod with mass m2 = 3.7 kg and length L = 2R = 0.4 m begins at rest above the disk and is dropped on the disk where it begins to spin with the disk. 1) What is the initial angular momentum of the rod and disk system? kg-m2/s Submit...
A system of two bodies consisting of a rod of mass m and length L, and a disk of mass M and radius R, moves in the x-y plane. The disk rotates about the axis attached to the rod at a distance b from its axis of rotation. The absolute angular velocity of the rod is 2, and the angular velocity of the disk relative to the rod is @. Determine the ratio E/Ho of the kinetic energy E of...
A thin disk (radius R and mass M) attached to the top of a hollow cylinder (height & radius R and mass M) is wobbling while spinning. ←R-height-radius Derive an expression for the angular momentum L of the object lif its initial rotation vector ω ω|êut ω3ез. Assume that ω3 is large and nonzero, that ω! İs nonzero but small, and that ω2 is initially zero A thin disk (radius R and mass M) attached to the top of a...
4. The figure below shows a hoop with mass m = 0.5 kg and radius a at rest on a frictionless table. Right a disk with mass M = 2m and radius b spinning with angular velocity W = 5.0 rad/s, and it is dropped onto the hoop. Eventually, the hoop and the disk rotate together with angular velocity 0. a. What is w? Express it in terms of a and b. (12 pts) b. How much energy AE is...