A rod is lying on the top of a table. One end of the rod is...

A rod is lying on the top of a table. One end of the rod is hinged to the table so that the rod can rotate freely on the tabletop. Two forces, both parallel to the tabletop, act on the rod at the same place. One force is directed perpendicular to the rod and has a magnitude of 38.0 N. The second force has a magnitude of 55.0 N and is directed at an angle with respect to the rod. If the sum of the torques due to the two forces is zero, what must be the angle ?

Key Concepts

Torque

Torque, or the moment of a force, is the rotational equivalent of linear force. It is calculated as the product of the force magnitude, the distance from the pivot point (lever arm), and the sine of the angle between the force vector and the lever arm. This concept explains how forces cause rotational motion and is crucial in problems where forces produce turning effects about a pivot.

Rotational Equilibrium

Rotational equilibrium occurs when the sum of all torques acting on an object is zero, meaning there is no net angular acceleration. In such a state, the clockwise torques balance the counterclockwise torques, ensuring that the object remains at rest or rotates at a constant rate. This principle is essential for analyzing systems where multiple forces act at various angles and distances from the pivot.

Lever Arm

The lever arm is the perpendicular distance from the axis of rotation (or pivot) to the line of action of the force. It is a key factor in determining the magnitude of the torque generated by a force. Understanding the lever arm helps in breaking down the effect of a force based on its point of application relative to the pivot.

Force Decomposition

Force decomposition involves breaking a force into its orthogonal components, typically along directions parallel and perpendicular to a given reference. In problems where a force is applied at an angle, resolving it into components allows for the calculation of its effective contribution to torque. This method is fundamental in simplifying complex force systems into manageable parts for analysis.

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