Home
Class 11
PHYSICS
A rod AB of length l is pivoted at an en...

A rod AB of length l is pivoted at an end A and freely rotated in a horizontal plane at an angular speed `omega` about a vertical axis passing through A. If coefficient of linear expansion of material of rod is `alpha`, find the percentage change in its angular velocity if temperature of system is incresed by `DeltaT`

Text Solution

Verified by Experts

If temperature of surrounding increases by `DeltaT`, the new length of rod becomes l. = `l(1+alphaDeltaT)`
Due to change in length, moment of inertia of rod also changes and moment of inertia about an end A and is given as `I_(A).=(Ml^(2))/3`
As no external force or torque is acting on rod, its angular momentum remains constant during heating.
Thus we have `I_(A)omega=I_(A).omega.` [where omega. is the final angular velocity of rod after heating]
or `(Ml^(2))/3omega=(Ml^(2)(1+alphaDeltaT)^(2))/3omega.`
or `omega.=omega(1-2alphaDeltaT)`
[using binomial expansion for small `alpha`]
Thus percentage change in angular velocity of rod due to heating can be given as
`Deltaomega=(omega-omega)/omegaxx100%=-2alphaDeltaTxx100%`
Promotional Banner

Similar Questions

Explore conceptually related problems

A uniform rod of mass m and length l rotates in a horizontal plane with an angular velocity omega about a vertical axis passing through one end. The tension in the rod at a distance x from the axis is

A uniform rod of length l is being rotated in a horizontal plane with a constant angular speed about an axis passing through one of its ends. If the tension generated in the rod due to rotation is T(x) at a distance x from the axis. Then which of the following graphs depicts it most closely?

A uniform rod of length l is from rest such that it rotates about a smooth pivot. The angular speed of the rod when it becomes vertical is. .

A uniform rod of mass m and length l_(0) is rotating with a constant angular speed omega about a vertical axis passing through its point of suspension. Find the moment of inertia of the rod about the axis of rotation if it make an angle theta to the vertical (axis of rotation).

Two balls of masses m and 2m are attached to the ends of a light rod of length L . The rod rotates with an angular speed omega about an axis passing through the center of mass of system and perpendicular to the plane. Find the angular momentum of the system about the axis of rotation.

A rod of length l is perpendicular to the lines of induction of a uniform magnetic field of induction B. The rod revolves at an angular speed omega about an axis passing through the rod's end parallel to the lines of induction. Find the voltage across the rod's ends.

A uniform rod of mass m and length L is hinged about one end and can freely rotate in a vertical plane. The angular velocity of the rod, when it falls from position P to Q. through an angle alpha starting from rest, is

A rod of length L is hinged from one end. It is brought to a horizontal position and released. The angular velocity of the rod, when it is in vertical position, is

A thin uniform copper rod of length l and mass m rotates uniformly with an angular velocity omega in a horizontal plane about a vertical axis passing through one of its ends. Determine the tension in the rod as a function of the distance r from the rotation axis. Find the elongation of the rod.

A rod is rotating with angular velocity omega about axis AB. Find costheta .