Key Terms

angular acceleration

time rate of change of angular velocity

angular position

angle a body has rotated through in a fixed coordinate system

angular velocity

time rate of change of angular position

instantaneous angular acceleration

derivative of angular velocity with respect to time

instantaneous angular velocity

derivative of angular position with respect to time

kinematics of rotational motion

describes the relationships among rotation angle, angular velocity, angular acceleration, and time

lever arm

perpendicular distance from the line that the force vector lies on to a given axis

linear mass density

the mass per unit length $\lambda$ of a one dimensional object

moment of inertia

rotational mass of rigid bodies that relates to how easy or hard it will be to change the angular velocity of the rotating rigid body

Newton’s second law for rotation

sum of the torques on a rotating system equals its moment of inertia times its angular acceleration

parallel axis

axis of rotation that is parallel to an axis about which the moment of inertia of an object is known

parallel-axis theorem

if the moment of inertia is known for a given axis, it can be found for any axis parallel to it

rotational dynamics

analysis of rotational motion using the net torque and moment of inertia to find the angular acceleration

rotational kinetic energy

kinetic energy due to the rotation of an object; this is part of its total kinetic energy

rotational work

work done on a rigid body due to the sum of the torques integrated over the angle through with the body rotates

surface mass density

mass per unit area $\sigma$ of a two dimensional object

torque

cross product of a force and a lever arm to a given axis

total linear acceleration

vector sum of the centripetal acceleration vector and the tangential acceleration vector