Glossary
Angular Momentum
A measure of the rotational inertia of a rotating object multiplied by its angular velocity. It is conserved in the absence of external torques.
Example:
A spinning ice skater conserves her angular momentum by changing her rotational inertia, which affects her angular velocity.
Angular Momentum
A measure of the rotational inertia of a rotating object multiplied by its angular velocity. It is a vector quantity that describes an object's tendency to continue rotating.
Example:
A spinning ice skater conserves their angular momentum as they pull their arms in, increasing their angular velocity.
Angular Velocity
The rate at which an object rotates or revolves relative to another point, measured in radians per second. It describes how fast an object is spinning.
Example:
A record player spins at a constant angular velocity of 33 1/3 revolutions per minute, which needs to be converted to radians per second for physics calculations.
Angular Velocity (ω)
The rate at which an object rotates or revolves relative to another point, measured in radians per second. It describes how fast an object is spinning.
Example:
A fast-spinning carousel has a high angular velocity, causing riders to feel a strong outward pull.
Center of Mass
The unique point where the weighted average of all the masses of a system is located. It's the point where the entire mass of the object can be considered to be concentrated for translational motion.
Example:
When you throw a baseball, its entire trajectory can be analyzed by tracking the motion of its center of mass.
Center of Mass
The unique point where the weighted average of all the mass of a system is located. For rigid objects, translational motion is described by the motion of this point.
Example:
When throwing a wrench, its complex motion can be simplified by tracking the path of its center of mass.
Conservation of Energy
A fundamental principle stating that the total energy of an isolated system remains constant over time, though it can transform from one form to another.
Example:
As a roller coaster goes down a hill, its potential energy is converted into kinetic energy, but the total mechanical energy remains conserved (ignoring friction).
Conservation of Energy
A fundamental principle stating that the total mechanical energy of a system remains constant if only conservative forces do work. This includes the interplay between potential, translational, and rotational kinetic energy.
Example:
When a roller coaster car descends a hill, its potential energy is converted into kinetic energy, demonstrating the principle of conservation of energy.
Rigid Object
An object whose shape and size do not change under the application of forces. In mechanics, it's often used to simplify analysis of rotational motion.
Example:
A spinning bicycle wheel can be modeled as a rigid object for analyzing its rotational dynamics.
Rigid System
A system of particles where the distance between any two particles remains constant, meaning the system does not deform.
Example:
A spinning bicycle wheel can be approximated as a rigid system because its shape doesn't change as it rotates.
Rotational Inertia
A measure of an object's resistance to changes in its rotational motion, analogous to mass in linear motion. It depends on the object's mass distribution relative to the axis of rotation.
Example:
A figure skater pulls their arms in to decrease their rotational inertia, allowing them to spin much faster.
Rotational Inertia (I)
A measure of an object's resistance to changes in its rotational motion. It depends on the object's mass distribution relative to the axis of rotation.
Example:
A hollow sphere has a larger rotational inertia than a solid sphere of the same mass and radius, making it harder to get spinning.
Rotational Kinetic Energy
The energy an object possesses due to its rotation. It represents the energy stored in a spinning object.
Example:
A spinning figure skater has rotational kinetic energy, even if she's not moving across the ice.
Rotational Kinetic Energy
The energy an object possesses due to its rotation. It quantifies the energy stored in a spinning object's motion.
Example:
A spinning flywheel stores a significant amount of rotational kinetic energy, which can be used to power machinery.
Scalar Quantity
A physical quantity that has magnitude but no direction.
Example:
Temperature is a scalar quantity; it only has a value, like 25°C, not a direction.
Scalar Quantity
A physical quantity that has magnitude but no direction. Rotational kinetic energy is an example, simplifying calculations as it can be added directly.
Example:
Temperature is a scalar quantity; it only has a value, like 25°C, without a direction.
Torque
A twisting force that tends to cause rotation. It is the rotational equivalent of linear force and is responsible for changes in angular momentum or rotational kinetic energy.
Example:
Applying a torque to a stubborn bolt with a wrench helps to loosen it.
Total Kinetic Energy
The sum of an object's rotational kinetic energy and its translational kinetic energy. For objects that are both spinning and moving linearly, this represents their complete kinetic energy.
Example:
A bowling ball rolling down the lane has total kinetic energy from both its forward motion and its spin.
Translational Kinetic Energy
The energy an object possesses due to its linear motion, dependent on its mass and linear velocity.
Example:
A car driving down a straight road possesses translational kinetic energy.
Translational Kinetic Energy
The energy an object possesses due to its linear motion. It is associated with the movement of an object's center of mass.
Example:
A car moving down a straight road primarily possesses translational kinetic energy.
Work-Energy Theorem
States that the net work done on an object equals the change in its kinetic energy. For rotational systems, work done by a torque changes rotational kinetic energy.
Example:
The Work-Energy Theorem can be used to find the final speed of a block after a force has pushed it over a certain distance.