Studied by 3 peopleangular acceleration, α
time rate of change of angular velocity
angular position, θ
angle a body has rotated through in a fixed coordinate system
angular velocity, ω
time rate of change of angular position
instantaneous angular acceleration, α
derivative of angular velocity with respect to time
instantaneous angular velocity, ω
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, r⊥
perpendicular distance from the line that the force vector lies on to a given axis
linear mass density, λ
the mass per unit length of a one-dimensional object
moment of inertia, I
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, K
kinetic energy due to the rotation of an object; this is part of its total kinetic energy
rotational work, W
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, σ
mass per unit area of a two-dimensional object
torque, τ
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
work-energy theorem for rotation
the total rotational work done on a rigid body is equal to the change in rotational kinetic energy of the body
right
The angular velocity ω is found using the ________-hand rule. If the fingers curl in the direction of rotation about a fixed axis, the thumb points in the direction of ω. The direction of angular acceleration can be determined by whether it is decreasing or increasing the magnitude of the angular velocity.
rotational
For every formula in translation motion there is a analogous __________ formula, where all angles are measured in radians.
mass, mass
Moments of inertia can be found by summing or integrating over every 'piece of _______' that makes up an object, multiplied by the square of the distance of each 'piece of _______' to the axis.
larger
Moment of inertia is ________ when an object's mass is farther from the axis of rotation
sum
Moment of inertia for a compound object is simply the _______ of the moments of inertia for each individual object that makes up the compound object.
right
The sign of the torque is found using the ________-hand rule.
Note
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