SSM ILW The body in Fig. 10-39 is pivoted at O, and two...

SSM ILW The body in Fig. $10-39$ is pivoted at $O,$ and two forces act on it as shown. If $r_{1}=1.30 \mathrm{m}, \quad r_{2}=2.15 \mathrm{m}, \quad F_{1}=$ $4.20 \mathrm{N}, F_{2}=4.90 \mathrm{N}, \theta_{1}=75.0^{\circ}$ and $\theta_{2}=60.0^{\circ},$ what is the net torque about the pivot?

SSM ILW The body in
Fig. $10-39$ is pivoted at $O,$ and
two forces act on it as shown. If
$r_{1}=1.30 \mathrm{m}, \quad r_{2}=2.15 \mathrm{m}, \quad F_{1}=$
$4.20 \mathrm{N}, F_{2}=4.90 \mathrm{N}, \theta_{1}=75.0^{\circ}$
and $\theta_{2}=60.0^{\circ},$ what is the net
torque about the pivot?

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Key Concepts

Torque

Torque is a measure of the rotational effect produced by a force acting at a distance from a pivot point. It is defined as the product of the force, the distance from the pivot (lever arm), and the sine of the angle between the force direction and the lever arm, characterizing how effectively the force causes rotational motion.

Lever Arm

The lever arm is the perpendicular distance from the line of action of the force to the pivot point. It plays a critical role in determining the magnitude of the torque, as a longer lever arm generally increases the torque produced by the same force.

Angle Between Force and Lever Arm

The angle between the force vector and the lever arm affects the portion of the force that contributes to rotation. Only the component of the force perpendicular to the lever arm (determined by the sine of the angle) produces torque, making this angle essential in torque calculations.

Net Torque Summation

Net torque is the algebraic sum of all individual torques acting on a body about a common pivot. It includes both magnitude and direction, where torques causing rotation in one direction are considered positive and those in the opposite direction are negative. This summation determines the overall rotational effect on the object.

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