The body in Fig. 10-39 is pivoted at O, and two forces act...

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

Key Concepts

Net Torque

Net torque is the sum of all individual torques acting on a body about a particular pivot point. It determines the overall rotational effect on the object, indicating whether the body will tend to rotate clockwise or counterclockwise. Calculating net torque involves accounting for both the magnitude and the direction (using a sign convention) of each torque.

Force Decomposition

In problems involving forces applied at angles, it is necessary to decompose the force into components. The component perpendicular to the lever arm is responsible for creating torque. This decomposition is essential for accurately calculating the effective contribution of a force to rotational motion.

Torque Sign Convention

The torque sign convention differentiates between torques that cause clockwise and counterclockwise rotations. By assigning positive or negative values to torques based on their rotational direction, it becomes possible to accurately sum multiple torques to find the net torque acting on an object.

Torque

Torque is a measure of the rotational force applied to an object. It is defined as the product of the force magnitude, the distance from the pivot point (lever arm), and the sine of the angle between the force direction and the lever arm. This concept is central in understanding rotational dynamics because it quantifies how effectively a force can cause an object to rotate.

Lever Arm

The lever arm is the perpendicular distance from the axis of rotation to the line of action of the force. It is a critical part of the torque calculation, as a larger lever arm allows a force to produce more rotational effect, emphasizing the importance of where the force is applied relative to the pivot.

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