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Lecture 23: Curvilinear Coordinates (RHB 8.10) It is often convenient to work with variables other than the Cartesian coordinates x. i( = x, y, z). For example in Lecture 15 we met spherical polar and cylindrical polar coordinates.
Homework Problem 2. Calculate the centroid of the composite shape in reference to the bottom of the shape and calculate the moment of inertia about the centroid z-axis.
CURVILINEAR MOTION: GENERAL & RECTANGULAR COMPONENTS. Today’s Objectives: Students will be able to: Describe the motion of a particle traveling along a curved path. Relate kinematic quantities in terms of the rectangular components of the vectors. In-Class Activities: Check Homework. Reading Quiz. Applications. General Curvilinear Motion.
The position vector of the first particle is given by r1(t) = rP + mt = (rPx + mxt)i + (rPy + myt)j, whereas the position vector of the second particle is given by r2(t) = rP + mt2 = (rPx + mxt2)i + (rPy + myt2)j. Clearly the path for these two particles is the same, but the speed at which each particle moves along the path is different.
The formula v = r is true for a wheel spinning about a fixed axis, where v is speed of points on rim. A similar formulas v CM = r works for a wheel rolling on the ground. Two very different situations, different v’s: v = speed of rim vs. v cm = speed of axis. But v = r true for both.
In this section, we determine how to calculate the angular momentum and kinetic energy of a rigid body, and define two important quantities: (1) the center of mass of a rigid body (which you already know), and (2) the Inertia tensor (matrix) of a. rigid body.
the satellite is directed towards the center of the circle, that is, along the radially inward direction.
