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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 λλ 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 σσ of a two dimensional object
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
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