Advertisements
Advertisements
प्रश्न
What is the relation between torque and angular momentum?
Advertisements
उत्तर
We have the expression for the magnitude of angular momentum of a rigid body as, L = I ω.
The expression for the magnitude of the torque on a rigid body is, τ = I α.
We can further write the expression for torque as,
`tau = "l"(domega)/(dt) (∴ α = (dω)/dt)`
Where ω is angular velocity and α is angular acceleration.
We can also write the equation,
`tau = (d(Iomega))/(dt)`
`tau = (dL)/(dt)`
APPEARS IN
संबंधित प्रश्न
A thin walled hollow cylinder is rolling down an incline, without slipping. At any instant, without slipping. At any instant, the ratio "Rotational K.E.: Translational K.E.: Total K.E." is ______.
While driving along an unbanked circular road, a two-wheeler rider has to lean with the vertical. Why is it so? With what angle the rider has to lean? Derive the relevant expression. Why such a leaning is not necessary for a four wheeler?
Answer in Brief:
A flywheel used to prepare earthenware pots is set into rotation at 100 rpm. It is in the form of a disc of mass 10 kg and a radius 0.4 m. A lump of clay (to be taken equivalent to a particle) of mass 1.6 kg falls on it and adheres to it at a certain distance x from the center. Calculate x if the wheel now rotates at 80 rpm.
Does the angle of banking depend on the mass of the vehicle?
A hollow sphere has a radius of 6.4 m. what is the minimum velocity required by a motorcyclist at the bottom to complete the circle.
Derive an expression for maximum safety speed with which a vehicle should move along a curved horizontal road. State the significance of it.
A railway track goes around a curve having a radius of curvature of 1 km. The distance between the rails is 1 m. Find the elevation of the outer rail above the inner rail so that there is no side pressure against the rails when a train goes around the curve at 36 km/hr.
A rigid body rotates with an angular momentum L. If its kinetic energy is halved, the angular momentum becomes, ______
A wheel of radius 2 cm is at rest on the horizontal surface. A point P on the circumference of the wheel is in contact with the horizontal surface. When the wheel rolls without slipping on the surface, the displacement of point P after half rotation of wheel is ______.
What is the difference between rotation and revolution?
