Glossary
Angular Acceleration (α)
The rate of change of angular velocity, indicating how quickly an object's rotational speed is increasing or decreasing. It is directly proportional to the net torque and inversely proportional to the moment of inertia.
Example:
When a potter's wheel is sped up, it experiences a positive angular acceleration as its rotational speed increases.
Angular Velocity (ω)
The rate at which an object changes its angular position, indicating how fast and in what direction it is rotating. It is typically measured in radians per second.
Example:
The blades of a helicopter have a high angular velocity when the helicopter is taking off, indicating how quickly they are spinning.
Conservation of Mechanical Energy
A fundamental principle stating that in an isolated system where only conservative forces (like gravity or spring force) do work, the total mechanical energy (sum of translational kinetic, rotational kinetic, and potential energies) remains constant.
Example:
As a yo-yo unwinds and rolls down its string, its gravitational potential energy is converted into both translational and rotational kinetic energy, demonstrating the conservation of mechanical energy.
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 object's total mass and how that mass is distributed relative to the axis of rotation.
Example:
It's much harder to spin a long pole about its center than about one end because its moment of inertia is significantly larger when rotating around its center.
Rigid Body Diagrams
Visual representations that show all external forces acting on an object, specifically indicating their points of application. These diagrams are crucial for accurately calculating torques and analyzing rotational motion.
Example:
To analyze the forces on a seesaw, a rigid body diagram would show the weights of the children at their specific distances from the pivot, along with the normal force at the pivot.
Rolling (without slipping)
A type of motion where an object simultaneously rotates and translates such that the point of contact with the surface has zero instantaneous velocity. In this ideal scenario, static friction does no work.
Example:
A bicycle wheel moving forward on a flat road without skidding is an example of rolling (without slipping), where the bottom of the tire momentarily stops relative to the ground.
Rotational Dynamic Equilibrium
The state where the net torque acting on an object is zero, resulting in either a constant angular velocity or no rotation at all. It is the rotational equivalent of Newton's First Law.
Example:
A balanced mobile hanging motionless from the ceiling is in rotational dynamic equilibrium because the torques from all its hanging parts cancel out.
Rotational Kinetic Energy (KE_rot)
The energy an object possesses due to its rotation around an axis. It is directly proportional to the object's moment of inertia and the square of its angular velocity.
Example:
A spinning top possesses rotational kinetic energy, which keeps it upright and rotating until friction eventually brings it to rest.
Sliding
A type of motion where an object translates across a surface without rotating, or where the point of contact has a non-zero instantaneous velocity relative to the surface. Kinetic friction typically acts and does work in this case.
Example:
When a hockey puck glides across the ice, it is sliding because it translates without significant rotation, and kinetic friction acts to slow it down.
Torque (τ)
A twisting force that causes or tends to cause rotation around an axis. Its magnitude depends on the applied force, the distance from the axis of rotation, and the angle between the force and the lever arm.
Example:
Using a long wrench to loosen a tight bolt provides greater torque than a short wrench, making the task easier due to increased leverage.