Glossary
Angular Acceleration
The rate of change of angular velocity, indicating how quickly an object's rotational speed is increasing or decreasing.
Example:
When a car's engine revs up, the crankshaft experiences angular acceleration.
Angular Impulse
The product of torque and the time interval over which it acts, which causes a change in an object's angular momentum.
Example:
Kicking a soccer ball off-center for a longer duration imparts a greater angular impulse, making it spin more.
Angular Momentum
The rotational equivalent of linear momentum, representing an object's tendency to continue rotating. For a rigid object, it is the product of its moment of inertia and angular velocity.
Example:
A figure skater spins faster when they pull their arms inward, demonstrating the conservation of angular momentum.
Angular Velocity
The rate at which an object rotates or revolves relative to another point, typically measured in radians per second.
Example:
A merry-go-round spinning at 2 revolutions per second has a high angular velocity.
Angular acceleration (α)
The rate of change of angular velocity, indicating how quickly an object's rotational speed is increasing or decreasing.
Example:
When a car's engine revs up, the crankshaft experiences angular acceleration.
Angular impulse
The rotational equivalent of linear impulse, measuring the change in angular momentum caused by a torque acting over a time interval. It is the integral of torque with respect to time.
Example:
Applying a brief, strong torque to a bicycle wheel to make it spin faster imparts an angular impulse.
Angular momentum
A measure of an object's tendency to continue rotating, analogous to linear momentum for translational motion. It is a vector quantity.
Example:
A spinning top maintains its upright position due to its significant angular momentum.
Angular velocity (ω)
The rate at which an object rotates or revolves about an axis, measured in radians per second (rad/s). It is a vector quantity.
Example:
A merry-go-round spinning quickly has a high angular velocity.
Area under a torque vs. time graph
Represents the total angular impulse delivered to an object over a given time interval.
Example:
By calculating the area under a torque vs. time graph for a spinning top, you can find the total change in its angular momentum.
Change in angular momentum (ΔL)
The difference between an object's final and initial angular momenta, representing the net effect of angular impulses.
Example:
When a figure skater pulls their arms in, their change in angular momentum is zero if no external torques act, leading to an increase in angular velocity.
Cross product
A binary operation on two vectors in three-dimensional space that results in a third vector perpendicular to the plane containing the first two vectors. It is used to calculate angular momentum (L = r x p).
Example:
Calculating the cross product of the position vector and the linear momentum vector of a satellite orbiting Earth gives its angular momentum.
Final Angular Momentum
The angular momentum of a rotating object at the end of a specific time period or process.
Example:
After a spinning top slows down due to friction, its final angular momentum will be less than its initial value.
Impulse-Momentum Theorem for Rotation
A fundamental principle stating that the angular impulse applied to an object is equal to the change in its angular momentum.
Example:
A sudden brake application on a bicycle wheel creates an angular impulse that reduces the wheel's angular momentum to zero, illustrating the theorem.
Impulse-Momentum Theorem for Rotation
States that the angular impulse applied to an object equals the change in its angular momentum. This theorem connects torque, time, and angular momentum.
Example:
The Impulse-Momentum Theorem for Rotation can be used to determine how long a motor needs to apply a certain torque to bring a flywheel up to a desired rotational speed.
Initial Angular Momentum
The angular momentum of a rotating object at the beginning of a specific time period or process.
Example:
Before a diver begins to tuck, their initial angular momentum is relatively low.
Linear momentum vector (p)
The product of an object's mass and its velocity, representing its tendency to continue moving in a straight line. It is a vector quantity.
Example:
A bowling ball rolling down the lane has a significant linear momentum vector in the direction of its motion.
Moment of Inertia
A measure of an object's resistance to changes in its rotational motion, depending on its mass and how that mass is distributed relative to the axis of rotation.
Example:
It's harder to spin a long pole around its end than around its center because of its higher moment of inertia about the end.
Moment of inertia (I)
A measure of an object's resistance to changes in its rotational motion, analogous to mass in linear motion. It depends on the mass distribution relative to the axis of rotation.
Example:
A long, thin rod has a larger moment of inertia when rotated about its end compared to its center, making it harder to spin.
Net Torque
The vector sum of all torques acting on an object, which determines its angular acceleration.
Example:
If two people push on opposite sides of a revolving door with equal force, the net torque is zero, and the door doesn't accelerate.
Net torque (τ_net)
The vector sum of all external torques acting on an object, which determines its angular acceleration.
Example:
If two people push on opposite sides of a merry-go-round with equal and opposite forces, the net torque is zero, and it won't start spinning.
Position vector (r)
A vector that defines the position of a point in space relative to an origin or reference point. In angular momentum calculations, it points from the reference point to the object.
Example:
When calculating the angular momentum of a ball thrown past you, the position vector extends from your chosen reference point to the ball's current location.
Right-hand rule
A mnemonic rule used to determine the direction of the angular momentum vector or the resulting vector from a cross product.
Example:
To find the direction of the angular momentum of a spinning bicycle wheel, curl your fingers in the direction of rotation, and your thumb will point in the direction given by the right-hand rule.
Slope of an angular momentum vs. time graph
Represents the net torque acting on an object at a given instant.
Example:
If the slope of an angular momentum vs. time graph is constant and positive, it indicates a constant net torque causing the object to speed up its rotation.
Time Interval
The duration over which a physical process or event occurs, often denoted as Δt.
Example:
The time interval a baseball bat is in contact with the ball determines the impulse imparted.
Torque
A rotational force that tends to cause an object to rotate or change its rotational motion, calculated as the product of force and the perpendicular distance from the pivot.
Example:
Using a long wrench to loosen a stubborn bolt applies more torque than a short wrench.
Torque (τ)
A rotational force that tends to cause an object to rotate or change its rotational motion. It is the rotational equivalent of force.
Example:
Using a wrench to tighten a bolt applies torque to the bolt, causing it to turn.
Vector quantity
A physical quantity that possesses both magnitude and direction. Angular momentum is an example of a vector quantity.
Example:
When a planet orbits the sun, its angular momentum is a vector quantity pointing perpendicular to its orbital plane.