JEE Main Systems of Particles and Rotational Motion: related Physics practice
Revise Systems of Particles and Rotational Motion with the original worked examples below. The practice bank below covers broader Physics topics; a dedicated Systems of Particles and Rotational Motion lesson is not available yet.
System of Particles and Rotational Motion: quick revision
Separate translation of the centre of mass from rotation about a chosen axis. Moment of inertia depends on that axis. A torque changes angular momentum; angular momentum is conserved when the net external torque about the chosen origin is zero.
Key ideas and when to use them
$x_{\rm cm}=\sum m_ix_i/\sum m_i$.
$\tau=rF\sin\theta$; for a rigid body about a fixed principal axis, $\tau=I\alpha$.
Rotational kinetic energy: $K=\tfrac12I\omega^2$.
Common mistakes
Use the perpendicular lever arm when calculating torque.
A change of rotation axis can change I even when the body is unchanged.
Three worked examples
Example 1: A rigid body has moment of inertia 0.50 kg·m² about its rotation axis and angular speed 4 rad/s. Find its rotational kinetic energy.
Use the moment of inertia about the stated axis.
$K=\tfrac12\times0.50\times4^2$.
4 J
Example 2: A 10 N force has a perpendicular lever arm of 0.30 m. Find its torque magnitude.
The perpendicular lever arm already includes the angle factor.
$\tau=10\times0.30$.
3 N·m
Example 3: Masses 2 kg and 3 kg lie at x = 0 m and x = 10 m. Find their centre of mass.
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