Glossary
Angular Acceleration
The rate at which an object's angular velocity changes over time. It is caused by a non-zero net torque.
Example:
When a car's engine revs up, the crankshaft experiences angular acceleration as its rotational speed increases.
Angular Acceleration
The rate of change of angular velocity over time, indicating how quickly an object's rotational speed is increasing or decreasing.
Example:
As a merry-go-round speeds up from rest, it experiences angular acceleration.
Angular Momentum
A measure of the amount of rotational motion an object has, calculated as the product of its moment of inertia and angular velocity (L = Iω).
Example:
A planet orbiting the sun possesses angular momentum due to its orbital motion.
Axis of Rotation
The imaginary line or point around which an object rotates. All torques and angular quantities are calculated relative to this axis.
Example:
For a spinning merry-go-round, the central pole acts as its axis of rotation.
Conservation of Angular Momentum
In the absence of external torques, the total angular momentum (L = Iω) of a system remains constant.
Example:
A figure skater pulling their arms in while spinning demonstrates the conservation of angular momentum, as their angular velocity increases while their moment of inertia decreases.
Constant Angular Velocity
A state where an object's angular speed and direction of rotation remain unchanged. It is a key characteristic of rotational equilibrium.
Example:
A record player spinning a vinyl at 33 1/3 RPM demonstrates constant angular velocity.
Constant Angular Velocity
The rate at which an object rotates or revolves remains unchanged over time, indicating no angular acceleration.
Example:
A record player spinning at 33 1/3 RPM has a constant angular velocity.
Fixed-Axis Rotation
A type of rotational motion where the axis of rotation remains stationary in space. AP Physics 1 primarily focuses on this type of rotation.
Example:
A door opening and closing on its hinges is an example of fixed-axis rotation.
Force Diagram
A diagram that specifically focuses on forces acting at a particular point or about an axis of rotation, often used to analyze torques.
Example:
When analyzing a lever, a force diagram helps identify the distances and directions of forces relative to the pivot point.
Free-Body Diagram
A diagram that illustrates all external forces acting on an object, typically represented as vectors originating from the object's center of mass.
Example:
Before solving a problem about a block on an incline, always draw a free-body diagram to visualize gravity, normal force, and friction.
Free-Body Diagram
A visual representation of all external forces acting on an object, used to analyze its linear motion.
Example:
To analyze a block sliding down an incline, you would draw a free-body diagram showing gravity, normal force, and friction.
Moment of 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 and the chosen axis of rotation.
Example:
A figure skater pulls their arms in to decrease their moment of inertia, allowing them to spin faster.
Moment of Inertia
A measure of an object's resistance to changes in its rotational motion, analogous to mass in linear motion, and dependent on mass distribution and the axis of rotation.
Example:
A solid disk has a smaller moment of inertia than a hoop of the same mass and radius, making it easier to rotate.
Net Torque
The vector sum of all individual torques acting on an object about a chosen axis of rotation. For rotational equilibrium, the net torque must be zero.
Example:
If you push on a door near the hinges and someone else pushes with equal force near the handle, the net torque on the door might still be non-zero if the forces are not balanced.
Net Torque
The vector sum of all individual torques acting on an object, determining its angular acceleration.
Example:
If a door is pushed from two sides with equal and opposite torques, the net torque is zero, and the door remains stationary.
Newton's First Law for Rotation
An object maintains a constant angular velocity (or remains at rest rotationally) unless acted upon by a non-zero net torque.
Example:
A bicycle wheel, once spun, continues to rotate at a steady rate until friction or air resistance creates a net torque to slow it down, illustrating Newton's First Law for Rotation.
Newton's First Law for Rotation
An object maintains a constant angular velocity (or remains at rest) if no net torque acts on it.
Example:
A bicycle wheel, once spun, continues to rotate at a steady rate due to Newton's First Law for Rotation until friction and air resistance create a net torque.
Newton's Second Law for Rotation
States that the net torque acting on an object is directly proportional to its angular acceleration and its moment of inertia ($\sum \vec{ au} = I \vec{\alpha}$).
Example:
When a mechanic uses a wrench to tighten a bolt, the applied torque causes the bolt to undergo angular acceleration according to Newton's Second Law for Rotation.
Newton's Second Law for Rotation
An unbalanced net torque causes a change in angular velocity (angular acceleration), proportional to the net torque and inversely proportional to the moment of inertia (Στ = Iα).
Example:
When a car engine applies a net torque to the wheels, it causes them to undergo angular acceleration, making the car speed up, as described by Newton's Second Law for Rotation.
Newton's Third Law for Rotation
States that for every torque exerted by one object on a second object, the second object exerts an equal and opposite torque on the first object.
Example:
When you twist a doorknob, the doorknob exerts an equal and opposite torque back on your hand, illustrating Newton's Third Law for Rotation.
Pivot Point
The fixed point or axis around which an object rotates or about which torques are calculated.
Example:
When opening a door, the hinges act as the pivot point.
Relationship to Linear Motion
Describes how angular quantities (angular velocity ω, angular acceleration α) relate to linear quantities (linear velocity v, linear acceleration a) for a point on a rotating object through the radius (v = rω, a = rα).
Example:
For a point on the edge of a spinning wheel, its linear speed is directly proportional to the wheel's angular speed and the wheel's radius, illustrating the relationship to linear motion.
Right-Hand Rule for Torque
A convention used to determine the direction of the torque vector. Point fingers in the direction of the position vector ($\vec{r}$), curl them towards the force vector ($\vec{F}$), and your thumb will point in the direction of the torque.
Example:
Using the Right-Hand Rule for Torque, you can determine if a force applied to a spinning top will make it precess clockwise or counterclockwise.
Rotational Equilibrium
The state where an object maintains a constant angular velocity, meaning its rate of rotation does not change. This occurs when the net torque acting on the object is zero.
Example:
A ceiling fan spinning at its highest setting is in rotational equilibrium because its blades are rotating at a steady speed.
Rotational Equilibrium
A state where an object maintains a constant angular velocity, meaning the net torque acting on it is zero.
Example:
A ceiling fan spinning at a steady speed is in rotational equilibrium because the motor's torque is balanced by air resistance.
Torque
The rotational equivalent of force, which causes or tends to cause rotation. It is calculated as the cross product of the position vector from the axis of rotation to the point of force application and the force vector ($\vec{ au} = \vec{r} imes \vec{F}$).
Example:
Applying a force to the end of a wrench creates a torque that can loosen or tighten a bolt.
Torque
A twisting force that tends to cause rotation, calculated as the product of the force, the distance from the pivot, and the sine of the angle between them (τ = rFsinθ).
Example:
Applying a force to the end of a wrench to tighten a bolt creates a torque that rotates the bolt.
Torque Diagram
A diagram that shows both the forces acting on an object and their respective distances from a chosen pivot point, used to analyze rotational motion.
Example:
When analyzing a seesaw, a torque diagram helps visualize how the weights of children on either side create torques about the pivot.
Translational Equilibrium
The state where an object maintains a constant linear velocity, meaning its center of mass is either at rest or moving at a constant speed in a straight line. This occurs when the net force acting on the object is zero.
Example:
A car cruising at a steady 60 mph on a straight highway is in translational equilibrium.
Translational Equilibrium
A state where an object's linear velocity is constant (which can be zero), meaning the net force acting on it is zero.
Example:
A car cruising at a steady 60 mph on a straight highway is in translational equilibrium.
Work-Energy Theorem (Rotational)
States that the net work done by torques on a rotating object equals the change in its rotational kinetic energy (1/2 Iω²).
Example:
The work done by a motor on a spinning flywheel can be calculated using the Work-Energy Theorem (Rotational) to find its final rotational speed.