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 $C$.

Show that when a metal rod $L$ meters long moves at speed $v$ perpendicular to $\vec{B}$ field lines, the magnetic force exerted by the field on the electrically charged particles in the rod produces a potential difference between the ends of the rod equal to the product $B L v$.

An aluminum rod is measured with a steel tape at $20^{\circ} \mathrm{C},$ and the length of the rod is found to be 75 cm. What length will the tape indicate when both the rod and the tape are at (a) $-10^{\circ} \mathrm{C}?$ (b) $50^{\circ} \mathrm{C} ?$

Determine the reactions at $A$ and $B$ when $a=7.5 \mathrm{~in}$.

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 assembly, consisting of the solid sphere of mass m and the uniform rod of length 2c and equal mass m, revolves about the vertical z-axis with an angular velocity $\omega$. The rod of length 2c has a diameter which is small compared with its length and is perpendicular to the horizontal rod to which it is welded with the inclination $\beta$. Determine the combined angular momentum $H_O$ of the sphere and inclined 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.

$$\delta(x)= \begin{cases}2-x, & 0 \leq x<1 \\ x, & 1 \leq x \leq 2\end{cases}$$

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.

The frame of mass 6m is initially at rest. A particle of mass m is attached to the end of the light rod, which pivots freely at A. If the rod is released from rest in the horizontal position, determine the velocity $v_{rel}$ of the particle with respect to the frame when the rod is vertical.

A 0.200-kg metal rod carrying a current of 10.0 A glides on two horizontal rails 0.500 m apart. What vertical magnetic field is required to keep the rod moving at a constant speed if the coefficient of kinetic friction between the rod and rails is 0.100?

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?

What is the function of a lightning rod?

Determine a mass density $\rho$ so that the center of mass of a rod of length L will be at a distance L/4 from one end of 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.