Figure shows a lamina in x-y plane. Two axes z and z^' pass perpendicular to its plane. A force

step 1 In this question we will learn about some basic concepts of the Newton's loss of motion. The que

Figure shows a lamina in x-y plane. Two axes z and z^' pass...

Figure shows a lamina in $x-y$ plane. Two axes $z$ and $z^{\prime}$ pass perpendicular to its plane. A force $F$ acts in the plane of lamina at point $P$ as shown. Which of the following statements is incorrect? (The point $P$ is closer to $z^{\prime}$-axis than the $z$-axis). (a) Torque t caused by $F$ about $z$ axis is along $\hat{k}$. (b) Torque $\tau^{\prime}$ caused by $F$ about $z^{\prime}$ axis is along $-\hat{k}$. 'c) Torque caused by $F$ about $z$ axis is greater in magnitude than that about $z^{\prime}$ axis. d) Total torque is given by $\tau=\tau+\tau^{\prime}$.

Figure shows a lamina in $x-y$ plane. Two axes $z$ and $z^{\prime}$ pass perpendicular to its plane.
A force $F$ acts in the plane of lamina at point $P$ as shown. Which of the following statements is incorrect? (The point $P$ is closer to $z^{\prime}$-axis than the $z$-axis).
(a) Torque t caused by $F$ about $z$ axis is along $\hat{k}$.
(b) Torque $\tau^{\prime}$ caused by $F$ about $z^{\prime}$ axis is along $-\hat{k}$.
'c) Torque caused by $F$ about $z$ axis is greater in magnitude than that about $z^{\prime}$ axis.
d) Total torque is given by $\tau=\tau+\tau^{\prime}$.

Key Concepts

Torque

Torque is a vector quantity that represents the rotational effect produced by a force applied at some distance from an axis. It is calculated as the cross product of the lever-arm (position vector relative to the axis) and the force vector, giving both magnitude and direction to the rotational influence. Understanding torque is essential for analyzing how forces produce rotation about various axes.

Moment Arm

The moment arm is the perpendicular distance between the line of action of a force and the axis of rotation. It plays a crucial role because the magnitude of the torque is directly proportional to this distance. A longer moment arm allows a given force to produce more torque, which is central to comparing rotational effects about different axes.

Right-Hand Rule

The right-hand rule is a convention used to determine the direction of a torque vector resulting from a cross product. By aligning the fingers of the right hand with the lever-arm and curling them toward the force vector, the thumb points in the direction of the resulting torque. This rule is vital for consistently assigning positive or negative signs to torques in a coordinate system.

Superposition of Torques

The principle of the superposition of torques states that when multiple torques are acting on a system, the total torque is the vector sum of the individual torques. This concept is fundamental when analyzing complex mechanical systems, enabling the breakdown of rotational effects into contributions from different forces or about different axes.

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