Three-dimensional motion involves movement in three spatial dimensions, characterized by changes in position along the x, y, and z axes simultaneously.
Class 11 Physics
Systems of Particle & Rotational Motion
CBSE EXAM 2024-25
Write an expression for torque in three-dimensional motion. Hence write the expressions for the rectangular components of torque.
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Torque in three-dimensional motion refers to the rotational force which is brought about by applying a force at some distance from an axis of rotation. In this sense, torque may be interpreted as the result of a force applied to cause rotation about an axis. To describe torque in three dimensions we consider the position vector that extends from the axis of rotation to where the force is applied as well as the force vector. The torque, here, can then be represented by its rectangular components along the three axes.
The torque component in the x-direction is given by the product of the y-coordinate of the position vector and the z-component of the force minus the product of the z-coordinate of the position vector and the y-component of the force. The y-component of the torque is the z-coordinate of the position vector multiplied by the x-component of the force, minus the product of the x-coordinate of the position vector and the z-component of the force. Lastly, the z-component of torque comes from the x and y components of the position and force vectors. This approach allows for a detailed analysis of rotational motion in three dimensions.
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