A uniform disc is rolling on a horizontal surface. At a certain instant B is point of contact and A

English

Gujarati

Hindi

6.System of Particles and Rotational Motion

hard

$A$ uniform disc is rolling on a horizontal surface. At a certain instant $B$ is the point of contact and $A$ is at height $2R$ from ground, where $R$ is radius of disc.

The magnitude of the angular momentum of the disc about $B$ is thrice that about $A$.

The angular momentum of the disc about $A$ is anticlockwise.

The angular momentum of the disc about $B$ is clockwise

All of the above

Solution

Angular velocity of the disc about any point on itself is constant.

Moment of inertia of a disc about its central axis is given by, $I_{o}=m R^{2} / 2$

Moment of inertia of a disc about an axis passing through a point on it's circumference and parallel to it's central axis is, $I_{c}=I_{o}+m R^{2}=3 m R^{2} / 2$

Therefore angular momentum of disc about $B$ is thrice than that about $A$.

All points on the disc about points $A$ and $B$ rotate clockwise. Therefore, angular moments are clockwise.

Standard 11

Physics

A flywheel can rotate in order to store kinetic energy. The flywheel is a uniform disk made of a material with a density $\rho $ and tensile strength $\sigma $ (measured in Pascals), a radius $r$ , and a thickness $h$ . The flywheel is rotating at the maximum possible angular velocity so that it does not break. Which of the following expression correctly gives the maximum kinetic energy per kilogram that can be stored in the flywheel ? Assume that $\alpha $ is a dimensionless constant

hard

A particle is moving along a straight line with increasing speed. Its angular momentum about a fixed point on this line …………

easy

$A$ particle of mass $2\, kg$ located at the position $(\hat i + \hat j)$ $m$ has a velocity $2( + \hat i – \hat j + \hat k)m/s$. Its angular momentum about $z$ -axis in $kg-m^2/s$ is

medium

Obtain the relation between torque of a system of particles and angular moment.