A particle of mass 'm' is performing uniform | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(A) The kinetic energy $E$ of a particle in rotational motion is given by $E = \frac{1}{2} I \omega^2$.Angular momentum $L$ is defined as $L = I \omeg

Vedclass · Accepted Answer

$\frac{L^2}{2 mr^2}$

Vedclass · Answer

(A) The kinetic energy $E$ of a particle in rotational motion is given by $E = \frac{1}{2} I \omega^2$.Angular momentum $L$ is defined as $L = I \omega$,which implies $L^2 = I^2 \omega^2$.Substituting $\omega^2 = \frac{L^2}{I^2}$ into the kinetic energy equation,we get $E = \frac{1}{2} I \left( \frac{L^2}{I^2} \right) = \frac{L^2}{2I}$.For a particle of mass '$m$' moving in a circle of radius '$r$',the moment of inertia about the axis passing through the center is $I = mr^2$.Substituting $I = mr^2$ into the expression for kinetic energy,we get $E = \frac{L^2}{2(mr^2)} = \frac{L^2}{2 mr^2}$.

$A$ particle of mass '$m$' is performing uniform circular motion along a circular path of radius '$r$'. Its angular momentum about the axis passing through the centre and perpendicular to the plane is '$L$'. The kinetic energy of the particle is

Similar Questions

$A$ circular disc of mass $20 \ kg$ and radius $1 \ m$ is rotating about an axis passing through its center and perpendicular to its plane with an angular velocity of $2 \ rad \ s^{-1}$. Then the rotational kinetic energy of the disc is (in $J$)

$A$ flywheel is in the form of a solid circular disc with a mass of $72 \ kg$ and a radius of $0.5 \ m$. If it rotates at $70 \ rpm$,its rotational kinetic energy is ........ $J$.

If the rotational kinetic energy of an object is $50\%$ of its linear kinetic energy,then the object is:

$A$ spherical solid ball of $1\,kg$ mass and radius $30\,cm$ is rotating about an axis passing through its centre with an angular velocity of $50\,rad/s$. The kinetic energy of rotation is ......... $J$.

$A$ flywheel is in the form of a solid circular disc of mass $72 \ kg$ and radius of $0.5 \ m$. If it rotates at $70 \ r.p.m.$,then the rotational kinetic energy is approximately ....... $J$.

Vedclass Test Series

Exam Paper Generator

Online Exam Module