Glossary
Angular Acceleration
The rate of change of angular velocity, indicating how quickly an object's rotational speed or direction is changing. It is directly related to net torque and moment of inertia ($ au = I\alpha$).
Example:
When a bicycle wheel starts spinning from rest, it undergoes angular acceleration as the rider pedals harder.
Cross Product
A binary operation on two vectors that results in a vector perpendicular to both original vectors. It is used to calculate the vector torque from the position and force vectors ($\vec{ au} = \vec{r} imes \vec{F}$).
Example:
Calculating the cross product of the position vector and the force vector helps determine the direction and magnitude of the resulting torque.
Equilibrium
The state of an object where both the net force and the net torque acting on it are zero, resulting in no linear or rotational acceleration.
Example:
A bridge is designed to be in equilibrium, ensuring it remains stationary and stable under the weight of traffic and its own structure.
Lever Arm
The position vector from the axis of rotation to the point where the force is applied, often representing the perpendicular distance from the axis to the line of action of the force.
Example:
To maximize the lever arm when opening a heavy door, you should push as far away from the hinges as possible.
Moment of Inertia
Also known as rotational inertia, it is an object's resistance to changes in its rotational motion. It depends on the object's mass and how that mass is distributed around the axis of rotation.
Example:
A figure skater pulls their arms in to decrease their moment of inertia, allowing them to spin faster.
Parallel Axis Theorem
A theorem used to calculate an object's moment of inertia about any axis parallel to one that passes through its center of mass ($I = I_{cm} + Mh^2$).
Example:
To find the moment of inertia of a door rotating about its hinges (not its center), you would use the parallel axis theorem with the door's moment of inertia about its center of mass.
Pivot Point
The specific point or axis about which an object rotates or is considered to rotate when analyzing torques. Choosing this point strategically can simplify calculations.
Example:
When analyzing a seesaw, choosing the fulcrum as the pivot point simplifies calculations by eliminating the torque due to the normal force at that point.
Right-Hand Rule
A mnemonic rule used to determine the direction of the torque vector. Point fingers in the direction of the lever arm, curl them towards the force vector, and your thumb points in the direction of the torque.
Example:
Using the right-hand rule, you can quickly determine that a force pushing down on the right side of a seesaw creates a clockwise torque.
Rotational Equilibrium
The condition where the net torque acting on an object is zero, meaning the object has no angular acceleration.
Example:
A balanced mobile hanging motionless from the ceiling is in rotational equilibrium because the torques from all its hanging parts cancel out.
Torque
The rotational equivalent of force, causing an object to rotate around an axis. It is a vector quantity measured in Newton-meters (N·m).
Example:
When you use a wrench to tighten a bolt, the twisting force you apply creates torque that rotates the bolt.
Translational Equilibrium
The condition where the net force acting on an object is zero, meaning the object has no linear acceleration.
Example:
A car cruising at a constant velocity on a straight road is in translational equilibrium because the engine's thrust balances air resistance and friction.