A thin rod (mass 8.28 kg, length 8.04 m) is sitting on a horizontal, frictionless table....

A thin rod (mass 8.28 kg, length 8.04 m) is sitting on a horizontal, frictionless table. There is a 0.626 kg frog sitting on the very end of the rod; you can treat the frog as a point particle. Suddenly the frog jumps off at speed 4.75 m/s, moving horizontally and perpendicular to the rod. Find ω, the angular speed of the rod after the frog jumps off, in rad/s.

Solutions

Expert Solution

Initially the frog and rod are stationary. Hence initial momentum and angular momentum of the frog-rod system is zero.

When the frog (0.626 kg) jumps off with a speed of 4.75 m/s then the centre of mass of the rod moves in opposite direction such that the momentum of rod is equal and opposite to that of frog.

The velocity of centre of rod is V = 0.626 x 4.75 / 8.28 = 0.36 m/s

The rod not only translates but also rotates about centre of the rod with angular velocity .

The rod rotates about centre such that the angular momentum of rod with respect to centre is equal and opposite to that of the frog.

The angular momentum of the frog with respect to centre is L = mvr = 0.626 x 4.75 x 4.02

L = 11.95 kg-m2/s

(as length of the rod is 8.04m and frog jumps from one end then distance of frog from centre is 4.02 m)

The angular momentum of the rod with respect to centre is L = I = (Md2/12)

L = (8.28 x (8.04)2 / 12) = 44.6

Then 44.6 = 11.95 => = 0.268 rad/s

The angular speed of the rod after the frog jumps off is 0.27 rad/s.

genius_generous answered 1 year ago

Next > < Previous

Related Solutions

A uniform thin rod of length 0.4 m and mass 0.5 kg can rotate in a...

A uniform thin rod of length 0.4 m and mass 0.5 kg can rotate in a horizontal plane about a vertical axis on the left end of the rod. The rod is at rest when a 10.0-g bullet traveling in the horizontal plane of the rod is fired into the right end of the rod at an angle 90o with the rod. The bullet lodges in the rod and the angular velocity of the rod is 10 rad/s immediately after...

A thin copper rod has a mass per unit length of 0.1 kg/m. What is the...

A thin copper rod has a mass per unit length of 0.1 kg/m. What is the minimum current in the rod that would allow it to levitate above the ground in a magnetic field of magnitude 0.5 T? (g = 10.0 m/s2) 2.9 A 2.5 A 2.2 A 2.0 A 1.8 A

A 1.1 kg mass is held at rest on top of a frictionless and horizontal table....

A 1.1 kg mass is held at rest on top of a frictionless and horizontal table. A light string loops over a pulley which is in the shape of a 10 cm radius solid disk which has a mass of 1.1 kg. The light string then supports a mass of 1.1 kg which is hanging in air. The mass on the table is released and the suspended mass falls. What is the acceleration of the falling mass. What is the...

A uniform thin rod of length 0.812 m is hung from a horizontal nail passing through...

A uniform thin rod of length 0.812 m is hung from a horizontal nail passing through a small hole in the rod located 0.043 m from the rod\'s end. When the rod is set swinging about the nail at small amplitude, what is the period of oscillation?

A uniform thin rod of length 0.778 m is hung from a horizontal nail passing through...

A uniform thin rod of length 0.778 m is hung from a horizontal nail passing through a small hole in the rod located 0.057 m from the rod's end. When the rod is set swinging about the nail at small amplitude, what is the period of oscillation?

On a frictionless horizontal air table, puck A (with mass 0.245 kg ) is moving toward...

On a frictionless horizontal air table, puck A (with mass 0.245 kg ) is moving toward puck B (with mass 0.374 kg ), which is initially at rest. After the collision, puck A has velocity 0.118 m/s to the left, and puck B has velocity 0.655 m/s to the right. A: What was the speed vAi of puck A before the collision? B: Calculate ΔKΔKDeltaK, the change in the total kinetic energy of the system that occurs during the collision.

On a frictionless, horizontal air table, puck A (with mass 0.250 kg ) is moving toward...

On a frictionless, horizontal air table, puck A (with mass 0.250 kg ) is moving toward puck B (with mass 0.400 kg ), which is initially at rest. After the collision, puck A has a velocity of 0.150 m/s to the left, and puck B has a velocity of 0.620 m/s to the right. a.What was the speed of puck A before the collision? b. Calculate the change in the total kinetic energy of the system that occurs during the...

On a frictionless horizontal air table, puck A (with mass 0.255 kg ) is moving toward...

On a frictionless horizontal air table, puck A (with mass 0.255 kg ) is moving toward puck B (with mass 0.375 kg ), which is initially at rest. After the collision, puck A has velocity 0.117 m/s to the left, and puck B has velocity 0.650 m/s to the right. What was the speed vAi of puck A before the collision? Calculate ΔK, the change in the total kinetic energy of the system that occurs during the collision.

On a frictionless horizontal air table, puck A (with mass 0.245 kg ) is moving toward...

On a frictionless horizontal air table, puck A (with mass 0.245 kg ) is moving toward puck B (with mass 0.373 kg ), which is initially at rest. After the collision, puck A has velocity 0.118 m/s to the left, and puck B has velocity 0.647 m/s to the right. a. What was the speed vAi of puck A before the collision? b. Calculate ΔK, the change in the total kinetic energy of the system that occurs during the collision.

Attached to each end of a thin steel rod of length 1.10 m and mass 6.60...

Attached to each end of a thin steel rod of length 1.10 m and mass 6.60 kg is a small ball of mass 1.07 kg. The rod is constrained to rotate in a horizontal plane about a vertical axis through its midpoint. At a certain instant, it is rotating at 39.0 rev/s. Because of friction, it slows to a stop in 32.0 s. Assuming a constant retarding torque due to friction, find the following. A) Angular Acceleration rad/sec^2 B) Retarding...

Subjects