Shows a slender uniform rod with mass M and length L. It might be a baton held by a twirler in a marching band (without the rubber end caps). (a) Use integration to compute its moment of inertia about an axis through O, at an arbitrary distance h from one end. (b) Initially the rod is at rest. It is given a constant angular acceleration of magnitude α around the axis through O. Find how much work is done on the rod in a time t. (c) At time t, what is the linear acceleration of the point on the rod farthest from the axis?

While carrying a heavy box up the stairs,you set the box on a step and rest. then you pick up the box and carry it to the top of the stairs. describe these actions in terms of balanced and unbalanced forces acting on the box.

Find the steady-state temperature at the center of the plate = /2, = /2) for sums of w from n=1 to n=19 (only odd values). find the value of n for which the change in /2, /2) is less than 1% from the value at the previous n. at this point, we consider the solution converged. does the value of the temperature at the center seem reasonable? in this part, the values of x and y are constant scalar values. you should produce a plot of the value of n on the horizontal and the estimate of the temperature at the center of the plate on the vertical. b. using the value of n (or larger) that resulted in convergence in part (a), create a contourf plot of the temperature distribution across the entire plate. use enough spatial subdivisions to create a useful plot. comment on the results. hint: you need to determine what “x” and “y” values to use to make your t matrix. i recommend using a different number of x and y values. use enough x and y values so that the plot is “smooth”.

An impulse is the product of the on an object and time during which it is applied