Glossary
Cross-Product for Torque
The cross-product is a mathematical operation used to calculate torque as a vector quantity, given by the formula $\vec{ au} = \vec{r} imes \vec{F}$. It yields a vector perpendicular to both the position vector and the force vector.
Example:
To find the exact vector direction and magnitude of the torque on a spinning top, you would use the cross-product for torque between its position vector and the applied force.
Equilibrium (Rotational)
A state where the net torque acting on an object is zero, meaning the object is either at rest or rotating at a constant angular velocity. AP Physics 1 often focuses on static equilibrium (at rest).
Example:
A balanced mobile hanging from the ceiling is in equilibrium, with all the torques from its hanging parts canceling each other out.
Force Diagrams
Visual representations similar to free-body diagrams, specifically used for rotational motion to show the forces and their application points relative to an axis of rotation, helping to analyze torques.
Example:
Drawing a force diagram for a seesaw helps identify where each child's weight creates a torque about the pivot point.
Force Diagrams
Force diagrams are visual representations that show all forces acting on a system, including their magnitudes, directions, and points of application relative to an axis of rotation. They are crucial for analyzing rotational motion.
Example:
Before solving a problem involving a rotating beam, drawing a force diagram helps visualize where gravity, tension, and other forces are acting.
Lever Arm
The perpendicular distance from the axis of rotation to the line of action of the force. A longer lever arm generally results in greater torque.
Example:
Using a long wrench to loosen a stubborn bolt provides a greater lever arm, making the task easier.
Lever Arm
The lever arm is the perpendicular distance from the axis of rotation to the line of action of the force. A longer lever arm generally results in greater torque for the same force.
Example:
To easily lift a heavy rock with a pry bar, you'd want a long lever arm to maximize the torque you can apply.
Magnitude of Torque
The scalar value representing the strength of the rotational effect, calculated by multiplying the distance from the axis of rotation (r), the force (F), and the sine of the angle (θ) between the force and position vectors (τ = rFsinθ).
Example:
Calculating the magnitude of torque on a bicycle pedal involves knowing the rider's force, the length of the pedal arm, and the angle at which the force is applied.
Maximum Torque
The greatest possible torque achieved when the applied force is entirely perpendicular (90°) to the lever arm, resulting in sinθ = 1.
Example:
To achieve maximum torque when tightening a screw with a screwdriver, you push down and twist, ensuring your twisting force is perpendicular to the screwdriver's handle.
Perpendicular Force Component
The portion of an applied force that acts at a 90-degree angle to the lever arm or position vector, which is the only part of the force that contributes to causing rotation.
Example:
If you push a swing at an angle, only the perpendicular force component of your push will effectively make the swing move forward.
Perpendicular Force Component
This is the portion of an applied force that acts at a 90-degree angle to the lever arm. Only this component contributes to producing torque.
Example:
If you push a door at an angle, only the part of your push that is perpendicular to the door will effectively open it, demonstrating the perpendicular force component.
Position Vector ($\vec{r}$)
The position vector is a vector that points from the axis of rotation (pivot point) to the point where the force is applied. Its magnitude is the distance from the pivot to the force application point.
Example:
When calculating the torque on a bicycle pedal, the position vector would extend from the center of the crank arm to where your foot pushes on the pedal.
Right-Hand Rule
The Right-Hand Rule is a mnemonic used to determine the direction of the torque vector resulting from a cross-product. You point your fingers along the position vector, curl them towards the force vector, and your thumb indicates the direction of the torque.
Example:
Using the Right-Hand Rule, if you push down on the right side of a steering wheel, your thumb points into the page, indicating the direction of the torque.
Torque
The rotational equivalent of force, measuring how much a force causes an object to rotate. It's often described as the 'twist' applied to an object.
Example:
When you push a door open, the torque you apply makes it swing on its hinges.
Torque
Torque is the rotational equivalent of force, causing an object to rotate or change its rotational motion. It depends on the magnitude of the force, the distance from the axis of rotation, and the angle at which the force is applied.
Example:
When you use a wrench to tighten a bolt, the twisting action you apply is torque, which causes the bolt to rotate.
Zero Torque
Occurs when the applied force acts parallel (0° or 180°) to the position vector or passes directly through the axis of rotation, meaning it causes no rotational effect.
Example:
Pushing directly into the hinges of a door results in zero torque, as the force doesn't create any rotation.