PHY exam 3

• A number that indicates the effectiveness of a force at producing rotation.
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• From the definition of torque, the rotating tendency increases as F increases and as d increases, which explains why it is easier to rotate a door if we push at the doorknob rather than at a point close to the hinges.

• If we know , we can find  about any axis parallel to the center of mass axis
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• D is the distance from center of mass axis to the parallel axis.

To generate the parallel-axis theorem, suppose an object rotates about the z axis. The moment of inertia does not depend on how the mass is distributed along the z axis; the moment of inertia of a cylinder is independent of its length. Imagine collapsing the three-dimensional object into a planar object, graphically. In this imaginary process, all mass moves parallel to the z axis until it lies in the xy plane.

The total kinetic energy of a rolling object is the sum of the rotational kinetic energy about the center of mass and the translational kinetic energy of the center of mass.

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• The radius is perpendicular to the distance from the axis of rotation.

• We can define angular momentum even if the particle is not moving in a circular path. Even a particle moving in a straight line has angular momentum about any axis displaced from the path of the particle.
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The total angular momentum of a system is constant in both magnitude and direction if the net external torque acting on the system is zero, that is, if the system is isolated.

• An object wholly or partly immersed in fluid is buoyed up by a force equal to the weight of fluid displaced.
• The buoyant force is exerted by the fluid. It is not determined by properties of the object except for the amount of fluid displaced by the object.

• Case 1: Totally Submerged Object: When an object is totally submerged in a fluid of density, the volume of the displaced fluid is equal to the volume of the object.
• Case 2: Floating Object: When an object is only partially submerged, the upward buoyant force is balanced by the downward gravitational force acting on the object.

A pressure applied to an enclosed fluid is transferred undiminished to every point in the fluid and to the walls of the container.

• Bernoulli's equation shows that the pressure of a fluid decreases as the speed of the fluid increases.
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• Where P is pressure, v is speed, and y is height