The disk rolls without sliding on the fixed horizontal surface. At the instant shown, the instantaneous center of zero velocity for rod $A B$ would be located in which region? $(a)$ Region 1 $(b)$ Region 2 $(c)$ Region 3 $(d)$ Region 4 $(e)$ Region 5 $(f)$ Region 6

The slotted wheel rolls to the right without slipping, with a constant speed v = 2 ft/sec of its center O. Simultaneously, motion of the sliding block A is controlled by a mechanism not shown so that $\dot{x}=1.5 \mathrm{ft} / \mathrm{sec} \text { with } \ddot{x}=0$. Determine the magnitude of the acceleration of A for the instant when x = 6 in. and $\theta=30^{\circ}$.

A rectangular plate swings from arms of equal length as shown. What is the magnitude of the angular velocity of the plate? $(a)$ $0 \mathrm{rad} / \mathrm{s}$ $(b)$ $1 \mathrm{rad} / \mathrm{s}$ $(c)$ $2 \mathrm{rad} / \mathrm{s}$ $(d)$ $3 \mathrm{rad} / \mathrm{s}$ $(e)$ Need to know the location of the center of gravity.

Arm $A C B$ rotates about point $C$ with an angular velocity of $40\ \mathrm{rad} / \mathrm{s}$ counterclockwise. Two friction disks $A$ and $B$ are pinned at their centers to $\operatorname{arm} A C B$ as shown. Knowing that the disks roll without slipping at surfaces of contact, determine the angular velocity of $(a)$ disk $A,(b)$ disk $B$.

A logic chip used in a computer dissipates 3 W of power in an environment at $120^\circ F,$ and has a heat transfer surface area of $0.08 in^2$ Assuming the heat transfer from the surface to be uniform, determine (a) the amount of heat this chip dissipates during an eight-hour work day, in kWh, and (b) the heat flux on the surface of the chip, in $W/in^2$

A cylindrical tank is fully filled with water. In order to increase the flow from the tank, additional pressure is applied to the water surface by a compressor. For $P_0=0, P_0=5$ bar, and $P_0=10$ bar, find the hydrostatic force on the surface $A$ exerted by water.

Air enters a 16-cm-diameter pipe steadily at 200 kPa and 20$^\circ{}$C with a velocity of 5 m/s. Air is heated as it flows, and it leaves the pipe at 180 kPa and 40$^\circ{}$C. Determine (a) the volume flow rate of air at the inlet, (b) the mass flow rate of air, and (c) the velocity and volume flow rate at the exit.

Two convex objects are inside a large vacuum enclosure whose walls are maintained at $T_{3}=300 \mathrm{K}$. The objects have the same area, $0.2 \mathrm{m}^{2}$, and the same emissivity, 0.2. The view factor from object 1 to object 2 is $F_{12}=0.3$. Embedded in object 2 is a heater that generates 400 W. The temperature of object 1 is maintained at $T_{1}=200 \mathrm{K}$ by circulating a fluid through channels machined into it. At what rate must heat be supplied (or removed) by the fluid to maintain the desired temperature of object 1? What is the temperature of object 2?

Consider a cylindrical cavity of diameter D=100mm and depth L=50 mm whose sidewall and bottom are diffuse and gray with an emissivity of 0.6 and are at a uniform temperature of 1500 K. The top of the cavity is open and exposed to surroundings that are large and at 300 K. (a) Calculate the net radiation heat transfer from the cavity, treating the bottom and sidewall of the cavity as one surface $\left(q_{A}\right)$. (b) Calculate the net radiation heat transfer from the cavity, treating the bottom and sidewall of the cavity as two separate surfaces $\left(q_{B}\right)$. (c) Plot the percentage difference between $q_{A}$ and $q_{B}$ as a function of L over the range $5 \mathrm{mm} \leq L \leq 100 \mathrm{mm}$.

In the planetary gear system shown, the radius of gears $A, B, C$, and $D$ is $30 \mathrm{~mm}$ and the radius of the outer gear $E$ is $90 \mathrm{~mm}$. Knowing that gear $E$ has an angular velocity of $180 \mathrm{~rpm}$ clockwise and that the central gear $A$ has an angular velocity of $240 \mathrm{~rpm}$ clockwise, determine $(a)$ the angular velocity of each planetary gear, $(b)$ the angular velocity of the spider connecting the planetary gears.

In the planetary gear system shown, the radius of gears $A, B, C$, and $D$ is $a$ and the radius of the outer gear $E$ is $3 a$. Knowing that the angular velocity of gear $A$ is $\omega_A$ clockwise and that the outer gear $E$ is stationary, determine $(a)$ the angular velocity of each planetary gear, $(b)$ the angular velocity of the spider connecting the planetary gears.

Velocity sensors are placed on a satellite that is moving only in the $x y$ plane. Knowing that at the instant shown the unidirectional sensors measure $\left(v_A\right)_x=2 \mathrm{ft} / \mathrm{s},\left(v_B\right)_x=-0.333 \mathrm{ft} / \mathrm{s}$, and $\left(v_C\right)_x=-2 \mathrm{ft} / \mathrm{s}$, determine $(a)$ the angular velocity of the satellite, $(b)$ the velocity of point $B$.

The plate shown moves in the $x y$ plane. Knowing that $\left(v_A\right)_x=12$ in. $/ \mathrm{s}$, $\left(v_B\right)_x=-4$ in. $/ \mathrm{s}$, and $\left(v_C\right)_y=-24$ in./s, determine $(a)$ the angular velocity of the plate, $(b)$ the velocity of point $B$, $(c)$ the point of the plate with zero velocity.

A particle moves along line segments from the origin to the points (1,0,0), (1,2,1) ,(0,2,1) , and back to the origin under the influence of the force field F(x, y, z)=z²i+2xyj+4y²k