Question
State work energy theorem for rotational motion.

Answer

According to work energy theorem, work done will be reflected as change in rotational kinetic energy. Work done for a small angular displacement $\text{d}\theta\text{ is },\text{dW}=\tau\text{d}\theta$
$\text{W}=\int\tau\text{ d }\theta=\int\text{I }\alpha\text{ d }\theta$
$=\int\text{I }\text{d }\omega\frac{\text{d }\theta}{\text{dt}}=\int\text{I }\omega\text{ d }\omega$
$\text{W}=\int^\limits{\omega\text{f}}_\limits{\omega\text{f}}\text{I }\omega\text{ d }\omega=\text{I}\Bigg|\frac{\omega^2}{2}\Bigg|^{\omega\text{f}}_{\omega\text{i}}$
$\text{W}=\frac{1}{2}\text{I}(\omega^2_{\text{f}}-\omega^2_{\text{i}})$
It is the change in rotational kinetic energy.

Need a full question paper?

Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.

Start Generating Free

Similar questions

The centre of gravity of a body on the earth coincides with its centre of mass for a ‘small’ object whereas for an ‘extended’ object it may not. What is the qualitative meaning of ‘small’ and ‘extended’ in this regard?
For which of the following the two coincides? A building, a pond, a lake, a mountain?
List the salient features of heat radiations.
What is the period of revolution of Neptune around the sun, given that the diameter of its orbit is 30 times the diameter of the earth's orbit around the sun, both orbits being assumed to be circular? Taking the moon's orbit around earth to be r and mass of earth 81 times the mass of the moon, find the position of the point from the earth where the net gravitational field is zero.
An experimenter's diary reads as follows: "A charged particle is projected in a magnetic field of $(7.0\vec{\text{i}}-3.0\vec{\text{j}})\times10^{-3}\text{T}.$ The acceleration of the particle is found to be $(\vec{\text{i}}+7.0\vec{\text{j}})\times10\text{m/s}^{2\text{n}}.$ The number to the left of $\vec{\text{i}}$ in the last expression was not readable. What can this number be?
Suppose the rod in the previous problem has a mass of 1kg distributed uniformly over its length:
  1. Find the initial angular acceleration of the rod.
  2. Find the tension in the supports to the blocks of mass 2kg and 5kg.
A dumb-bell consists of two identical small balls of mass $\frac{1}{2}\text{kg}$ each connected to the two ends of a 50cm long light rod. The dumb-bell is rotating about a fixed axis through the centre of the rod and perpendicular to it at an angular speed of 10rad/s. An impulsive force of average magnitude 5.0N acts on one of the masses in the direction of its velocity for 0.10s. Find the new angular velocity of the system.
Suppose white light falls on a double slit but one slit is covered by a violet filter (allowing $\lambda=400\text{nm}$). Describe the nature of the fringe pattern observed.
A parallel-plate capacitor of plate-area A and plate separation d is joined to a battery of emf $\in$ and internal resistance R at t = 0. Consider a plane surface of area $\frac{\text{A}}{2}$ parallel to the plates and situated symmetrically between them. Find the displacement current through this surface as a function of time.
The driver of a truck travelling with a velocity v suddenly notices a brick wall in front of him at a distance d. Is it better for him to apply brakes or to make
a circular turn without applying brakes in order to just avoid crashing into the wall? Why?
A piece of copper having a rectangular cross-section of 15.2mm × 19.1mm is pulled in tension with 44,500N force, producing only elastic deformation. Calculate the resulting strain?