A metre stick is balanced on a knife edge at its centre....

A metre stick is balanced on a knife edge at its centre. When two coins, each of mass $5 \mathrm{~g}$ are put one on top of the other at the $12.0 \mathrm{~cm}$ mark, the stick is found to be balanced at $45.0 \mathrm{~cm}$. What is the mass of the metre stick?

Key Concepts

Torque

Torque is the measure of the tendency of a force to rotate an object about an axis or pivot. It is calculated as the product of the force applied and the perpendicular distance (moment arm) from the pivot to the point of application of the force. Understanding torque is essential when analyzing the conditions required for rotational balance in any mechanical system.

Rotational Equilibrium

Rotational equilibrium occurs when the net torque acting on a system about a pivot is zero, meaning there is no angular acceleration. This balance of torques ensures that the object remains in a steady state without rotating. Analyzing rotational equilibrium is key when addressing problems where forces are applied at different distances from a pivot.

Moment Arm

The moment arm, or lever arm, is the perpendicular distance from the axis of rotation or pivot to the line of action of the force. This concept is crucial because the magnitude of the torque produced by a force depends directly on the length of this moment arm. It enables one to calculate the influence of forces applied at various points along an object.

Center of Mass

The center of mass of an object is the average location of its mass distribution, often coinciding with its geometric center for uniform objects. It is the point at which gravity can be considered to act. In problems of balance, knowing the center of mass is important for determining the conditions for equilibrium, especially when additional masses are added to the system.

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