Chapter 11: Rolling, Torque & Angular Momentum Flashcards
The motion of a rigid body through three-dimensional space can be analyzed as two separate motions combined:
The translational motion of the COM and the rotational motion about an axis through the COM.
When rolling without slipping, the net velocity of the point at the top of the circle is ___ and the net velocity at the bottom of the circle is ___.
2v(subcom); 0.
Pure rotation is…
Movement only about the rotational axis with no translational motion.
Pure translation is…
Movement that occurs free of any rotational motion; solely translational motion.
The kinetic energy of rotation is given by the formula…
0.5I(subcom)ω^2
The kinetic energy of a rolling object is…
K(subroll) = K(subtrans) + K(subrotcom)
Acceleration of an object that rolls without slipping down an incline:
(gsinθ)/(1+(I(subcom)/(MR^2)))
When calculating the torque around a point, τ = ___, or the vector product of ___ and ___.
r × F; position; force.
Angular momentum is…
The momentum of a particle as it moves around a set rotational axis. l = r × p, with p being the linear momentum and r being the position vector.
Newton’s second law in angular form is as follows:
F(subnet) = ma OR ___ OR ___.
τ(subnet) = Iα OR ___ OR ___.
F = dp/dt; p = mv
τ(subnet) = dl/dt; l = r × p
The total angular momentum of a rigid body is equal to the sum of the ___ of all its constituent particles. OR; L = ___.
angular momenta; Iω
Newton’s second law for a non-particle rotating body:
τ(subnet) = dl/dt
A net external torque is required to change a body’s angular momentum, and the net external torque equals ___.
The rate of change of the angular momentum.
Newton’s second law for a rotating body has a very important consequence:
If the next external torque equals zero, then the angular momentum of that system is conserved.
If the derivative of the angular momentum is zero, then it (is)/(is not) constant.
Is.
