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Radius of Gyration

A rigid horiz...

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A rigid horizontal smooth rod `AB` of mass `0.75 kg` and length `40 cm` can rotate freely about a fixed vertical axis through its mid point `O`. Two rings each of mass `1 kg` are initially at rest at a distance of `10 cm` from `O` on either side of the rod. The rod is set in rotation with an angular velocity of `30` radian per second. Find the velocity of each ring along the length of the rod in `m/s` when they reach the ends

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Q. A rigid horizontal smooth rod AB of mass 0.75 Kg and length 40 cm can rotate freely about a fix verticle axis through its midpoint O.Two rings each of mass 1 kg initially at rest at a distance of 10 cm from O on either side of the rod. The rod is set in rotation with an angular velocity of 30 radians per second and when the rings reach the ends of the rod, the angular velocity in rad/ sec is:

Q. A ring which can slide along the rod is kept at the mid point of a smooth rod of length L. The rod is rotated with a constant angular velocity

ω

about vertical axis passing through one of its ends. Ring is released from mid point. Find the velocity of the ring when it just leave the rod.

Q. A horizontal smooth rod

A B

rotates with a constant angular velocity

ω = 2.00 r a d / s

about a vertical axis passing through its end

A

. A freely sliding sleeve of mass

m = 0.50 k g

moves along the rod from the point

A

with the initial velocity

v_{0} = 1.00 m / s

. Find the Coriolis force acting on the sleeve (in the reference frame fixed to the rotating rod) at the moment when the sleeve is located at the distance

r = 50 c m

from the rotation axis in Newton. (Round off to the nearest integer.)

Q. A uniform rod of mass in and length l can rotate freely on a smooth horizontal plane about a vertical axis hinged at point

H

. A point mass having same mass

m

coming with an initial speed

u

perpendicular to the rod, strikes the rod in elastically at its free end. Find out the angular velocity of the rod just after collision?

Q. A smooth uniform rod of length

L

M

has two identical beads of negligible size, each of mass

m

, which can slide freely along the rod. Initially the two beads are at the centre of the rod and the system is rotating with angular velocity

ω_{0}

about its axis perpendicular to the rod and passing through its mid point (see figure).There are no external forces. When the beads reach the ends of the rod, the angular velocity of the system is:

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