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State an example where an object has different rotating parts but dome of them have Rotational Kinetic Energy and some do not.
 Observe the following picture:
 The masses m do not have any Kinetic anergy because they do not travel through space and the masses M rotate around the y=axis
 There fore we can calculate the Moment of inertia I of the system and Rotational Kinetic Energy in the following way:

State the calculated Moment of Inertia I (kg m^{2}) for a thin sylindrical shell. (thin hoop)

State the calculated Moment of Inertia I (kg m2) for a Hollow Cylinder.

State the calculated Moment of Inertia I (kg m2) for a Solid cylinder or disk.

State the calculated Moment of Inertia I (kg m^{2}) for a Long, thin rod with rotation axis through center.

State the calculated Moment of Inertia I (kg m^{2}) for a long, thin rod with rotation axis through the end.

State the calculated Moment of Inertia I (kg m^{2}) for a solid sphere

State the calculated Moment of Inertia I (kg m^{2}) for a Thin spherical shell



Rolling with out slipping, explain.

State the mathematical formula to calculate the Kinetic Energy of an dylinder rolling with out slipping.
 Let us start with a picture:
 Notice that when the cylinder is rolling with out splipping the cylinder has two different types of kinetic (rolling) energies. One is translational and the other one rotational.
 In the formula for kinetic energy of a rolling cylinder the two kinetic energies must be consider.
 The first term represents the rotational kinetic energy of the objects about its center of mass, and the second term represents the kinetic energy the object would have if it were just translating throug space without totating. Therefore the total kinetic energy is the sum of the two.


Vector product operation (cross product) is a commutative operation. By this we mean:
AxB = BxA
True
False
 False
 False, the cross product operation is NOT commutative.


How can we calculate the Net external torque on a system?
 The net torque on a system equals the time rate of change of angular momentum of the system.


Calculate total Torque on a system using the Moment of inertia of an object and angular acceleration.
 Rotational form of Newton's Second Law.
 That is, the net external torque acting on a rigid object about a fixed axis equals the moment of inertia about the rotation axis multiplied gy the object's angular acceleration relative to that axis.


List the three quantities that remain constant on certain conditions. These three quanties one could say that are the only energies that of most likely conserved in an isolated system.
(if there are no energy tranfers acrros the system boundary.)
(if the nt external force on the system is zero)
(if the net external torque on the system is zero)

