A 50.0 -g meter stick is balanced at its midpoint (50.0 cm). Then a 0.100-kg and a 0.200-kg mas

step 1 In this question we have given that there is a uniform thin bar whose mass is 6m and length is 1

A 50.0 -g meter stick is balanced at its midpoint (50.0...

A $50.0$ -g meter stick is balanced at its midpoint $(50.0 \mathrm{~cm})$. Then a $0.100-\mathrm{kg}$ and a $0.200-\mathrm{kg}$ mass are hung with light string from the $10.0$ -cm and $70.0$ -cm points, respectively. (Figure 8-59). Calculate the clockwise and counterclockwise torques acting on the board due to the four forces shown about an axis pointing out of the page at the following points: (a) the $0-\mathrm{cm}$ point, (b) the 50 -cm point, and (c) the 100 -cm point. (d) Is the meter stick still balanced after the two masses have been added? Example 8-17

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Key Concepts

Center of Mass

The center of mass is the point at which an object’s mass is considered to be concentrated. In uniform objects, it often coincides with the geometric center, and it is crucial when determining the torque due to the object's weight.

Rotational Equilibrium

Rotational equilibrium occurs when the net torque acting on a system is zero, meaning that there is no overall rotational acceleration. This concept is key in analyzing balance and stability in a system where multiple torques are present.

Sign Convention for Torque

A proper sign convention is essential when calculating torques, as it distinguishes between torques causing clockwise and counterclockwise rotations. This helps ensure that torques are summed correctly to analyze the net effect on the system.

Torque

Torque is the measure of the force that produces rotation about an axis. It is calculated as the product of the force magnitude and the perpendicular distance (lever arm) from the axis of rotation. This fundamental concept explains how forces cause objects to rotate.

Lever Arm

The lever arm is the distance from the axis of rotation to the point where the force is applied. It determines how effective a force is at producing a torque; the longer the lever arm, the greater the torque for a given force.

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