Review of a college exam covering rotational motion, angular momentum, and fluid mechanics.
Table of Formulas
What is torque?
A number that indicates the effectiveness of a force at producing rotation.
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.
What is the parallel-axis theorem?
If we know , we can find about any axis parallel to the center of mass axis
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.
How do you find the total kinetic energy of a rotating object?
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.
How do you find the moment of inertia (I)?
The radius is perpendicular to the distance from the axis of rotation.
What is the definition of angular momentum?
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.
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.
Recite Archimedes' Principle
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.
What are the 2 cases of Archimedes' Principle?
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.
Recite Pascal's Law
A pressure applied to an enclosed fluid is transferred undiminished to every point in the fluid and to the walls of the container.
Recite Bernoulli's Principle
Bernoulli's equation shows that the pressure of a fluid decreases as the speed of the fluid increases.