Torque is a measure of the rotational force that causes an object to rotate about an axis, fulcrum, or pivot. It is the product of the force and the perpendicular distance between the line of action of the force and the axis of rotation. Torque is a crucial concept in the study of rotational motion and equilibrium.
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Torque is the rotational equivalent of force, just as angular acceleration is the rotational equivalent of linear acceleration.
The magnitude of torque is equal to the product of the force and the perpendicular distance from the line of action of the force to the axis of rotation.
The direction of the torque is determined by the right-hand rule, where the thumb points in the direction of the rotation and the fingers curl around the axis of rotation.
Torque is a vector quantity, meaning it has both magnitude and direction.
Torque is an important concept in the study of equilibrium, as an object is in equilibrium when the net torque acting on it is zero.
Review Questions
Explain how torque is calculated and how it relates to rotational motion.
Torque is calculated as the product of the force and the perpendicular distance from the line of action of the force to the axis of rotation. This relationship is expressed mathematically as $\tau = r \times F$, where $\tau$ is the torque, $r$ is the perpendicular distance, and $F$ is the force. Torque is the rotational equivalent of force, and it is the primary cause of rotational motion. When a net torque is applied to an object, it will experience an angular acceleration, causing it to rotate around the axis.
Describe the relationship between torque and equilibrium, and explain how the concept of the center of mass is relevant.
For an object to be in equilibrium, the net torque acting on it must be zero. This means that the sum of all the torques acting on the object must cancel out. The center of mass of an object is an important concept in the study of torque and equilibrium, as the location of the center of mass determines the point about which the object will rotate when a torque is applied. If the net force acting on an object is zero, but the net torque is non-zero, the object will experience rotational motion around its center of mass.
Analyze how the concept of a 'couple' relates to torque and the study of rotational motion and equilibrium.
A couple is a pair of equal, opposite, and non-collinear forces that create a torque without a net force. The torque created by a couple is independent of the location of the axis of rotation, as long as the axis is not between the two forces. Couples are important in the study of rotational motion and equilibrium because they can create a net torque without a net force, allowing an object to rotate without translating. This concept is particularly relevant in the analysis of static equilibrium, where the net force and net torque on an object must both be zero for the object to be in equilibrium.
The moment of a force is the product of the force and the perpendicular distance from the line of action of the force to the axis of rotation. Moment is another term for torque.
Couple: A couple is a pair of equal, opposite, and non-collinear forces that create a torque without a net force.
The center of mass is the point in an object or system of objects where the entire mass of the object or system can be considered to be concentrated. It is an important concept in the study of torque and moments.