2 Flashcards
(12 cards)
What is tangential velocity in terms of angular velocity?
The product of radial displacement and angular velocity.
What is tangential displacement in terms of angular displacement?
The product of radial displacement and angular displacement.
the integral of radial displacement with respect to angular displacement
What is tangential acceleration in terms of angular acceleration?
The product of radial displacement and angular acceleration?
What is the moment of inertia?
What is it analogous to?
Moment of inertia = the sum of (the product of mass and {radial displacement squared}).
Moment of inertia = the integral of radial displacement squared with respect to mass.
Analogous to mass.
What is an equation for the kinetic energy of a rotating body?
KE = 1/2 * (moment of inertia {I}) * (radial velocity)^2
What are three equations for torque?
What is torque analogous to?
Torque = the cross product of radial displacement and force.
Torque = the product of moment of inertia and angular acceleration.
Torque = to the rate of change of angular momentum.
Torque is analogous to force.
What are two equations for angular momentum? (on a particle relative to an origin)
What is angular momentum analogous to?
Angular momentum = the cross product of radial displacement and momentum.
Angular momentum = the product of moment of inertia and angular velocity.
Analogous to momentum.
What is the principle of conservation of angular momentum?
When the net external torque acting on a system is zero, the total angular momentum of the system remains constant.
Analogous to Newton’s first law.
What can a rolling body be thought of as?
A body undergoing both rotational and translational motion, where the velocity of the translational motion is equal to the tangential velocity of the rotational motion.
OR, the instantaneous rotation of the body about an axis parallel to the ground, where the wheel contacts the ground, with equal angular velocity to the rotational motion in the other interpretation.
What is an equation for the KE of a rolling body?
The sum of the rotational KE and the translational KE.
What is the “non-slip condition” for a rotating body?
The velocity of the centre of mass of the body is equal to the tangential velocity.
If this is not satisfied, the body is slipping, and kinetic friction will result in the condition being eventually satisfied.
What is the parallel axis theorem?
Relates the moment of inertia about an axis through the COM to the moment of inertia through a second parallel axis.
(moment of inertial through parallel axis) = (moment of inertia through COM axis) + (total mass * {distance between the two axis squared})
