One end of a metal rod is in contact with a thermal reservoir at 700 . $\mathrm{K}$, and the other end is in contact with a thermal reservoir at 100 . $\mathrm{K}$. The rod and reservoirs make up an isolated system. If 8500 . J are conducted from one end of the rod to the other uniformly (no change in temperature along the rod) what is the change in entropy of (c)the system?

Use the results of previous problem and determine the angular momentum $H_G$ of the bent rod of that problem about its mass center G using the given reference axes previous problem. The bent rod has a mass $\rho$ per unit length and rotates about the z-axis with an angular velocity $\omega$. Determine the angular momentum $H_O$ of the rod about the fixed origin O of the axes, which are attached to the rod. Also find the kinetic energy T of the rod.

Give density functions of thin rod lying along various interval of the x-axis. Use Equations (3a) through (3c) to find the rod's moment about the origin, mass, and center of mass.

$\delta(x)=3\left(x^{-3 / 2}+x^{-5 / 2}\right), \quad 0.25 \leq x \leq 1$

A thin uniform rod (length $=1.00 \mathrm{~m}$, mass $=2.00 \mathrm{~kg}$ ) is pivoted about a horizontal frictionless pin through one of its ends. The moment of inertia of the rod through this axis is $\frac{1}{3} m L^2$. The rod is released when it is $60.0^{\circ}$ below the horizontal. What is the angular acceleration of the rod at the instant it is released?

The left-hand end of a light rod of length L is attached to a vertical wall by a frictionless hinge. An object of mass m is suspended from the rod at a point a distance $\alpha \mathrm{L}$ from the hinge, where $0<\alpha \leq 1.00$. The rod is held in a horizontal position by a light wire that runs from the right-hand end of the rod to the wall. The wire makes an angle $\theta$ with the rod. What is the angle $\beta$ that the net force exerted by the hinge on the rod makes with the horizontal?

A solid aluminum $[E=70 \mathrm{GPa}]$ rod (1) is connected to a solid bronze $[E=100 \mathrm{GPa}]$ rod at flange $B$ as shown in Figure P5.32. Aluminum rod (1) has an outside diameter of $35 \mathrm{~mm}$, and bronze rod (2) has an outside diameter of $20 \mathrm{~mm}$. The normal stress in the aluminum rod must be limited to $160 \mathrm{MPa}$, and the normal stress in the bronze rod must be limited to $110 \mathrm{MPa}$. Determine (a) the maximum downward load $P$ that may be applied at flange $B$. (b) the deflection of flange $B$ at the load that you determined in part (a).

Laser light of wavelength 510 nm is traveling in air and shines at normal incidence onto the flat end of a transparent plastic rod that has n = 1.30. The end of the rod has a thin coating of a transparent material that has refractive index 1.65. What is the minimum (nonzero) thickness of the coating (a) for which there is maximum transmission of the light into the rod; (b) for which transmission into the rod is minimized?

A thin uniform rod (length $=1.00 \mathrm{~m}$, mass $=2.00 \mathrm{~kg}$ ) is pivoted about a horizontal frictionless pin through one of its ends. The moment of inertia of the rod through this axis is $\frac{1}{3} m L^2$. The rod is released when it is $60.0^{\circ}$ below the horizontal. What is the angular acceleration of the rod at the instant it is released ?

Suppose Fig. 32-36 shows a cylindrical rod whose end has a radius of curvature $R=2.0 \mathrm{~cm}$, and the rod is immersed in water with index of refraction of $1.33$. The rod has index of refraction 1.53. Find the location and height of the image of an object $2.0 \mathrm{~mm}$ high located $23 \mathrm{~cm}$ away from the rod.

A charge per unit length $\lambda$ is distributed uniformly along a thin rod of length $L$. (a) Determine the potential (chosen to be zero at infinity) at a point $P$ a distance $y$ from one end of the rod and in line with it as given in the figure. (b) Use the result of (a) to compute the component of the electric field at $P$ in the $y$ direction (along the rod). (c) Determine the component of the electric field at $P$ in a direction perpendicular to the rod.

A rod of length $L_{0}$ moves with a speed v along the horizontal direction. The rod makes an angle of $\theta_{0}$ with respect to the $x^{\prime} \text { -axis }$. (a) Show that the length of the rod as measured by a stationary observer is given by $L=L_{0}\left[1-\left(v^{2} / c^{2}\right) \cos ^{2} \theta_{0}\right]^{1 / 2}$. (b) Show that the angle that the rod makes with the x-axis is given by the expression $\tan \theta=\gamma \tan \theta_{0}$. These results show that the rod is both contracted and rotated. (Take the lower end of the rod to be at the origin of the primed coordinate system.)

The 23-in. vertical rod CD is welded to the midpoint C of the 50-in. rod AB. Determine the moment about AB of the 174-lb force Q.

Plastic and glass rods that have been charged by rubbing with wool and silk, respectively, hang by threads.
a. An object repels the plastic rod. Can you predict what it will do to the glass rod? If so, what? If not, why not? Explain.
b. A different object attracts the plastic rod. Can you predict what it will do to the glass rod? If so, what? If not, why not? Explain.

The lever $B C D$ is hinged at $C$ and attached to a control rod at $B$. If $P=100\ \mathrm{lb}$, determine $(a)$ the tension in $\operatorname{rod} A B,(b)$ the reaction at $C$.