The slender rod of mass m and length l rotates about the y-axis as the element of a right-circular cone. If the angular velocity about the y-axis is $\omega$, determine the expression for the angular momentum of the rod with respect to the x-y-z axes for the particular position.

For a short interval of motion, collar A moves along its fixed shaft with a velocity $v_A$ = 2 m/s in the Y-direction. Collar B, in turn, slides along its fixed vertical shaft. Link AB is 700 mm in length and can turn within the clevis at A to allow for the angular change between the clevises. For the instant when A passes the position where y = 200 mm, determine the velocity of collar B using nonrotating axes attached to B and find the component $\omega_n$, normal to AB, of the angular velocity of the link. Also solve for $v_B$ by differentiating the appropriate relation $x_2 + y_2 + z_2 = l_2$.

The uniform slender rod of mass m and length L is initially at rest in a centered horizontal position on the fixed circular surface of radius R = 0.6L. If a force P normal to the bar is gradually applied to its end until the bar begins to slip at the angle $\theta=20^{\circ}$, determine the coefficient of static friction $\mu_s$.

The long, straight wire shown in Fig. we saw earlier carries constant current $l$. A metal bar with length $L$ is moving at constant velocity $\overrightarrow{\boldsymbol{v}}$, as shown in the figure. Point $a$ is a distance $d$ from the wire. If the bar is replaced by a rectangular wire loop of resistance $R$, what is the magnitude of the current induced in the loop?

Determine the mass moments of inertia about the x-, y-, and z- axes of the slender rod of length L and mass m which makes an angle $\beta$ with the x-axis.

The mass of the uniform slender rod is 3 kg. Determine the position x for the 1.2 kg slider such that the system period is 1 s. Assume small oscillations about the horizontal equilibrium position.

A dielectric of permittivity $3.5 \times 10^{-11} \mathrm{F} / \mathrm{m}$ completely fills the volume between two capacitor plates. For t > 0 the electric flux through the dielectric is $\left(8.0 \times 10^{3} \vee \cdot \mathrm{m} / \mathrm{s}^{3}\right) t^{3}$. The dielectric is ideal and nonmagnetic; the conduction current in the dielectric is zero. At what time does the displacement current in the dielectric equal $21 \mu \mathrm{A}$?

The long, straight wire shown in Fig. we saw earlier carries constant current $l$. A metal bar with length $L$ is moving at constant velocity $\overrightarrow{\boldsymbol{v}}$, as shown in the figure. Point $a$ is a distance $d$ from the wire. Calculate the emf induced in the bar.

The long, straight wire shown in Fig. we saw earlier carries constant current $l$. A metal bar with length $L$ is moving at constant velocity $\overrightarrow{\boldsymbol{v}}$, as shown in the figure. Point $a$ is a distance $d$ from the wire. Which point, $a$ or $b$, is at higher potential?

The circular disk of 100-mm radius rotates about its z-axis at the constant speed p = 240 rev/min, and arm OCB rotates about the Y-axis at the constant speed N = 30 rev/min. Determine the velocity v and acceleration a of point A on the disk as it passes the position. Use reference axes x-y-z attached to the arm OCB.

A very long, cylindrical wire of radius $R$ carries a current $I_0$ uniformly distributed across the cross section of the wire. Calculate the magnetic flux through a rectangle that has one side of length $W$ running down the center of the wire and another side of length $R$, as shown in Fig. we saw earlier.

The wheel of radius r is free to rotate about the bent axle CO which turns about the vertical axis at the constant rate p rad/s. If the wheel rolls without slipping on the horizontal circle of radius R, determine the expressions for the angular velocity $\omega$ and angular acceleration $\alpha$ of the wheel. The x-axis is always horizontal.

Will a free market tend to encourage or discourage discrimination? Explain briefly.

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.