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is the rotational force that causes objects to spin. It's calculated using length, force magnitude, and angle. Understanding is crucial for grasping how things rotate in everyday life, from opening doors to using tools.

The helps determine torque direction, while net torque calculations reveal an object's rotational behavior. These concepts connect to broader ideas of rotational dynamics, energy, and momentum, essential for understanding mechanical systems.

Torque

Effects on torque magnitude

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Top images from around the web for Effects on torque magnitude

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  • Torque (τ\tau) causes an object to rotate about an axis calculated using the formula: τ=r×F=rFsin⁡θ\tau = r \times F = rF\sin\theta
    • rr represents the length measuring the distance from the axis of rotation to the point where force is applied
    • FF represents the magnitude of the force applied
    • θ\theta represents the angle between the force vector and the lever arm
  • Longer lever arm results in greater torque for the same applied force doubling the lever arm length doubles the torque assuming the force and angle remain constant (wrench, crowbar)
  • Force angle measured between the force vector and the lever arm affects torque magnitude
    • Torque maximized when the force is perpendicular to the lever arm (θ=90∘\theta = 90^\circ) in this case sin⁡θ=1\sin\theta = 1 so τ=rF\tau = rF (opening a door, using a wrench)
    • Torque zero when the force is parallel to the lever arm (θ=0∘\theta = 0^\circ or 180∘180^\circ) in this case sin⁡θ=0\sin\theta = 0 so τ=0\tau = 0 (pushing on a wall, pulling a rope)
    • For angles between 0∘0^\circ and 90∘90^\circ torque varies with sin⁡θ\sin\theta (pushing a lawn mower, rowing a boat)

Right-hand rule for torque direction

  • Right-hand rule determines the direction of the torque vector
    • Point right thumb in the direction of the lever arm from the axis of rotation to the point of force application
    • Curl fingers in the direction of the force
    • Thumb now points in the direction of the torque vector (opening a jar, turning a doorknob)
  • Torque vector perpendicular to both the lever arm and the force vector pointing along the axis of rotation
  • Counterclockwise torques considered positive clockwise torques considered negative (tightening a screw, loosening a bolt)

Calculation of net torque

  • Net torque sum of all individual torques acting on an object about a common axis τnet=τ1+τ2+τ3+...\tau_{net} = \tau_1 + \tau_2 + \tau_3 + ...
  • To calculate net torque:
    1. Choose a common axis of rotation
    2. Calculate each individual torque about that axis using τ=rFsin⁡θ\tau = rF\sin\theta
      • Use right-hand rule to determine the sign of each torque positive for counterclockwise negative for clockwise
    3. Sum all individual torques to find net torque
  • Net torque zero object in
    • Object will not rotate if initially at rest (balanced seesaw, steering wheel at rest)
    • Object will rotate with constant angular velocity if initially rotating (spinning top, ceiling fan)
  • Net torque non-zero object will experience in the direction of the net torque (opening a heavy door, starting a lawnmower engine)
    • This relationship is described by the

Rotational Dynamics and Energy

  • , also known as , measures an object's resistance to rotational acceleration
  • is the rotational analog of linear momentum, describing an object's tendency to continue rotating
  • The applies to rotational systems, relating the work done by torque to changes in rotational kinetic energy
  • is a fundamental principle in rotational dynamics, similar to conservation of linear momentum

Key Terms to Review (29)

Angular acceleration: Angular acceleration is the rate of change of angular velocity over time. It describes how quickly an object is rotating or spinning.
Angular Acceleration: Angular acceleration is the rate of change of angular velocity with respect to time. It describes the rotational analog of linear acceleration, quantifying the change in the rotational motion of an object around a fixed axis or point.
Angular momentum: Angular momentum is a measure of the quantity of rotation of an object and is a vector quantity. It is given by the product of the moment of inertia and angular velocity.
Angular Momentum: Angular momentum is a fundamental concept in physics that describes the rotational motion of an object. It is the measure of an object's rotational inertia and its tendency to continue rotating around a specific axis. Angular momentum is a vector quantity, meaning it has both magnitude and direction, and it plays a crucial role in understanding the behavior of rotating systems across various topics in physics.
Conservation of Angular Momentum: Conservation of angular momentum is a fundamental principle in physics that states the total angular momentum of a closed system remains constant unless an external torque is applied. This principle is essential in understanding the behavior of rotational motion and the dynamics of spinning objects.
Corkscrew right-hand rule: The corkscrew right-hand rule is a mnemonic used to determine the direction of the cross product vector in three-dimensional space. Point your right-hand thumb in the direction of the first vector and curl your fingers towards the second vector; your thumb points in the direction of the resulting vector.
Dynamometer: A dynamometer is a device used to measure the torque or rotational force produced by a rotating system, such as an engine or motor. It is a crucial tool for evaluating the performance and efficiency of various mechanical systems.
Frictional Torque: Frictional torque is the rotational force that opposes the motion of an object due to friction between two surfaces in contact. It is a crucial concept in understanding the dynamics of rotational motion and the behavior of mechanical systems.
Gravitational Torque: Gravitational torque is the rotational force exerted by the force of gravity on an object about a specific axis or point of rotation. It is a key concept in the study of rotational dynamics and is essential for understanding the behavior of objects under the influence of gravity.
Law of conservation of angular momentum: The law of conservation of angular momentum states that if no external torque acts on a system, the total angular momentum of the system remains constant. This principle is crucial in understanding rotational dynamics.
Lever arm: The lever arm is the perpendicular distance from the axis of rotation to the line of action of the force. It is a crucial factor in determining the torque produced by a force.
Lever Arm: The lever arm is the perpendicular distance from the axis of rotation or pivot point to the line of action of a force. It is a fundamental concept in understanding the effects of forces on objects in rotational equilibrium or when analyzing torque.
Moment of inertia: Moment of inertia is a measure of an object's resistance to changes in its rotational motion about a fixed axis. It depends on the mass distribution relative to the axis of rotation.
Moment of Inertia: The moment of inertia is a measure of an object's resistance to rotational acceleration. It is a scalar quantity that depends on the mass and distribution of an object's mass about a given axis of rotation. The moment of inertia is a crucial concept in the study of rotational dynamics, as it determines how an object will respond to applied torques.
N⋅m: N⋅m, or Newton-meter, is a unit of measurement that represents the product of force (in newtons) and distance (in meters). It is commonly used to quantify the concept of torque, which is the rotational force that causes an object to rotate about an axis, fulcrum, or pivot.
Newton-Meter: The newton-meter (N⋅m) is the unit used to measure torque, which is the rotational force that causes an object to rotate about an axis, pivot, or fulcrum. It is the product of the applied force and the perpendicular distance between the axis of rotation and the line of action of the force.
Newton's First Law: Newton's First Law, also known as the Law of Inertia, states that an object at rest will remain at rest, and an object in motion will continue moving at a constant velocity, unless acted upon by an unbalanced force. This fundamental principle describes the relationship between an object's state of motion and the forces acting upon it.
R × F: The cross product, denoted as r × F, is a vector operation that represents the torque acting on an object due to a force applied at a distance. It is a fundamental concept in the study of rotational dynamics and is essential for understanding the behavior of objects undergoing rotational motion.
RF sin θ: The term $rF \sin \theta$ represents the magnitude of the torque acting on an object. It is a crucial concept in the study of rotational dynamics and the analysis of rotational equilibrium.
Right-Hand Rule: The right-hand rule is a mnemonic device used to determine the direction of various vector quantities, such as the cross product of two vectors, the direction of torque, angular momentum, and the precession of a gyroscope. It provides a simple and intuitive way to visualize and remember the orientation of these physical quantities.
Rotational Equilibrium: Rotational equilibrium is a state where the net torque acting on an object is zero, resulting in the object's rotational motion remaining constant or the object remaining at rest. This concept is fundamental in understanding the behavior of rigid bodies under the influence of external forces.
Rotational Inertia: Rotational inertia, also known as moment of inertia, is a measure of an object's resistance to changes in its rotational motion. It is the rotational equivalent of linear inertia, which is a measure of an object's resistance to changes in its linear motion.
Torque: Torque is a measure of the rotational force applied to an object around a pivot point. It is calculated by the product of the force and the perpendicular distance from the pivot point to the line of action of the force.
Torque: Torque is a measure of the rotational force applied to an object, which causes it to rotate about an axis. It is influenced by the magnitude of the force applied, the distance from the axis of rotation, and the angle at which the force is applied, making it crucial for understanding rotational motion and equilibrium.
Torque Wrench: A torque wrench is a tool used to precisely measure and apply a specific amount of torque (rotational force) to a fastener, such as a nut or bolt, to ensure it is tightened to the proper specification. This tool is essential in applications where the proper tightness of a connection is critical for safety, function, or preventing damage.
Torque-Angular Acceleration Equation: The torque-angular acceleration equation describes the relationship between the torque applied to an object and the resulting angular acceleration of that object. This equation is a fundamental concept in rotational dynamics and is crucial for understanding the motion of rigid bodies under the influence of external forces.
Work-energy theorem: The work-energy theorem states that the net work done on an object is equal to its change in kinetic energy. Mathematically, it is expressed as $W_{net} = \Delta KE$.
Work-Energy Theorem: The work-energy theorem is a fundamental principle in physics that states the change in the kinetic energy of an object is equal to the net work done on that object. It establishes a direct relationship between the work performed on an object and the resulting change in its kinetic energy, providing a powerful tool for analyzing and solving problems involving energy transformations.
τ (Tau): Tau (τ) is a fundamental physical quantity that represents torque, which is the measure of the rotational force acting on an object. Torque is a vector quantity that describes the tendency of a force to cause rotational motion about a pivot, axis, or fulcrum. Tau is a crucial concept in the understanding of rotational dynamics and the precession of gyroscopes.
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Glossary
Glossary
10.7 Newton’s Second Law for Rotation