is a fundamental concept in rotational mechanics, measuring how forces cause objects to rotate around an axis. It's crucial for understanding everything from simple machines like levers to complex systems like engines and gears.
Mastering torque helps us analyze both static and dynamic rotational systems. We'll explore its mathematical expression, factors affecting it, and its applications in equilibrium, acceleration, and energy transfer in rotating objects.
Definition of torque
Torque plays a crucial role in rotational mechanics, extending the principles of linear force to objects that rotate around an axis
Understanding torque provides insights into how forces cause rotational motion, a fundamental concept in mechanical systems and engineering
Rotational force concept
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Top images from around the web for Rotational force concept
Torque and Angular Acceleration | Boundless Physics View original
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12.1 Conditions for Static Equilibrium | University Physics Volume 1 View original
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10.6 Torque | University Physics Volume 1 View original
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Torque and Angular Acceleration | Boundless Physics View original
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12.1 Conditions for Static Equilibrium | University Physics Volume 1 View original
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Torque measures the tendency of a force to rotate an object around a fixed axis
Calculated as the product of force magnitude and perpendicular distance from the axis of rotation
Determines the effectiveness of a force in causing
Analogous to how linear force causes translational acceleration in linear motion
Torque vs linear force
Linear force causes objects to move in straight lines, while torque causes rotational motion
Torque depends on both force magnitude and its point of application relative to the rotation axis
Can produce rotation even when the net linear force is zero (spinning wheel)
Measured in newton-meters (N·m) or pound-feet (lb·ft), unlike linear force measured in newtons (N) or pounds (lb)
Mathematical expression
Torque equation
Expressed mathematically as [τ = r × F](https://www.fiveableKeyTerm:τ_=_r_×_f) where τ is torque, r is the position vector, and F is the applied force
Cross product nature indicates torque is perpendicular to both r and F
Magnitude calculated using τ=rFsin(θ) where θ is the angle between r and F
Scalar form often used in practical applications τ=Fd where d is the perpendicular distance from the axis to the line of action of the force
Vector nature of torque
Torque is a pseudovector, pointing along the axis of rotation
Direction determined by the right-hand rule relative to the plane of rotation
Vector addition applies when multiple torques act on a system
Cross product in torque equation results in its vector nature, crucial for understanding 3D rotational dynamics
Factors affecting torque
Magnitude of force
Directly proportional relationship between force magnitude and resulting torque
Doubling the applied force doubles the torque, assuming other factors remain constant