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Concept
Torque is a measure of the rotational force applied to an object, which causes it to rotate around an axis or pivot point. It is calculated as the product of the force applied and the distance from the point of rotation, with the direction of the torque determined by the right-hand rule.
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The lever arm is the perpendicular distance from the axis of rotation to the line of action of the force, playing a crucial role in determining the torque produced by a force. Understanding lever arm is essential for analyzing mechanical systems and calculating the effectiveness of levers and other rotational devices.
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Perpendicular distance refers to the shortest distance from a point to a line or plane, measured along a line that is perpendicular to the line or plane. It is a fundamental concept in geometry and is used in various applications like calculating the area of triangles and determining the distance between skew lines in three-dimensional space.
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The axis of rotation is an imaginary line around which an object rotates, and it is crucial in determining the object's rotational dynamics. Understanding the axis of rotation helps in analyzing the stability, angular momentum, and torque of rotating bodies in both natural and engineered systems.
Newton's Second Law for Rotation states that the net torque acting on a rigid body is equal to the product of its moment of inertia and its angular acceleration. This law is the rotational analog of Newton's Second Law of Motion and is crucial for understanding how forces affect rotational motion.
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Concept
Rotational dynamics is the branch of physics that deals with the motion of objects that rotate around an axis, involving the study of torques and angular momentum. It helps explain phenomena ranging from the spin of a figure skater to the rotation of celestial bodies, providing a comprehensive understanding of rotational motion and its effects.
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A bending moment is the reaction induced in a structural element when an external force or moment is applied, causing the element to bend. It is a critical concept in structural engineering, determining the internal stresses that must be managed to prevent failure or deformation of the structure.
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The cross product is a binary operation on two vectors in three-dimensional space, resulting in a third vector that is perpendicular to the plane containing the original vectors. It is widely used in physics and engineering to determine torque, rotational effects, and to find a vector perpendicular to a plane defined by two vectors.
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A vector quantity is a physical measurement that has both magnitude and direction, distinguishing it from scalar quantities which have only magnitude. Vectors are crucial in fields like physics and engineering to describe quantities such as force, velocity, and displacement, and are typically represented graphically by arrows or mathematically by ordered pairs or triplets.
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Support reactions are the forces or moments generated at the supports or connections of a structure in response to external loads, ensuring equilibrium. They are essential for analyzing and designing structures, as they help determine the internal forces and moments within the structure.
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