A uniform cylinder of radius 14 cm and mass 27 kg is mounted so as to rotate freely about a horizontal axis that is parallel to and 9.3 cm from the central longitudinal axis of the cylinder. (a) What is the rotational inertia of the cylinder about the axis of rotation? (b) If the cylinder is released from rest with its central longitudinal axis at the same height as the axis about which the cylinder rotates, what is the angular speed of the cylinder as it passes through its lowest position?

A 100 pF capacitor has circular plates of 10.0 cm radius that are 5.0 mm apart and have air beteween them. The capacitor is charged by connecting it to a 12.0 V battery through a 1.0 ohms resistor.

a) Determine the current through the plates at t = 0 (when the battery is connected)

b) Determine the current through the plates at t = 60s?

c) Determine the rate at which the electric field between the plates changes at t= 0 and t = 60s

d) Determine the magnetic field between the plates at t = 0 and at t = 60s

Don't really care about the answers as much, but more about what formulas are being used.

Thanks!

Two parallel conducting plates are oriented in an ? − ? coordinate system. The plates are separated by a distance ? = 0.05 ?, and the origin of the coordinate system is halfway between the plates. The plate separation is very small compared to the size of the plates. The left plate is at a potential ?_L = 50 ?, and the right plate is at a potential ?_R = 10 ?.

1. A proton at the origin begins at rest. Use conservation of energy to find its velocity when it hits one of the plates. Which plate does it hit?

2. An electron at the origin begins with an initial velocity ?⃗? = (4 × 106 ?/?)?̂. Use conservation of energy to find its velocity when it hits the right plate?

3. What is the acceleration of a proton at the origin? Express your answer in unit vector notation.

3. What is the acceleration of a proton at the origin? Express your answer in unit vector notation.

which of the following motions should be correctly analyzed using the torque version of Newton's 2nd law? Circle all that apply.

a. a car slows to a stop as it approaches a traffic light on a straight road.

b. a car travels around a circular path.

c. a car travels around a circular path on a banked road.

d. the tires of a car spin at a constant rate as the car goes around a curve.

10) A solid disk with a c of 1/2, mass of 2 kg, and radius of 1.4 meters lies on a horizontally (so the normal force and weight can be ignored). A force of 9 Newtons is applied 0.37 meters directly to the right of center in the +x direction, a force of 25 Newtons is applied 0.80 meters directly below of center in the +x direction, and a force of 9 Newtons is applied at the edge of the disk directly above the center in the +x direction. Again, ignoring the weight and normal force, if the disk starts from rest, what is the angular velocity of the disk after these forces are applied for 3 seconds, in rad/s? If clockwise, include a negative sign.

Coefficient of drag (flat plate, NASA) = C(d) = 1.28

Weight = W = 4451 lbs

Gravitation constant = g = 32.2 ft/sec^2

Area = A = 197.5"" long x 78.2"" wide x (1 ft^2/ 14 in^2)

Vehicle falls flat, wheels 1st, straight down, at constant acceleration with no aerodynamic drag until terminal velocity

Horsepower needed to accelerate is AVERAGE - not peak

100% driveline efficiency

A hydrogen-rich gas stream contains 1.0 mole % carbon monoxide. It is desired to use a microporous ceramic membrane for separating carbon monoxide (CO) from hydrogen gas at a pressure of 1 atm and a temperature of 400C. The average pore diameter of the membrane is 15 nm and the void fraction is 0.30.

a) Estimate the molecular diffusivity of CO in a mixture with H2

b) Determine the Knudsen diffusion coefficient and the effective diffusion coefficient for CO in the membrane

In the “race” of conceptual problem 5 (and similar to what we did in lab), the uniform cylinder, uniform sphere, and cylindrical hoop race down a 2 meter long ramp tilted 10^o to the horizontal. Each object has the same mass (10.0 kg) and radius (10.0 cm). Assume no slippage between the ramp and object and the coefficient of friction = 0.5. Calculate the following: (a) the final velocity of each (b) the center of mass acceleration of each object, (c), the time required for each object to race down the ramp, (d) the frictional force acting on each object. Fill in the table below with the numerical values (but make sure you show how you obtained the necessary relationships!).

A wheel turns through 2.1 revolutions while accelerating from rest at 16 rpm/s.

What is its final angular speed?

How long does it take?

The rearview mirror of a car is a convex mirror (R = -15 m). Consider the image formed by a car that is 10 m from the mirror.

1. A convex mirror means that the mirror has a _positive/ negative_ radius of curvature. So, the center of curvature and

   focal length are located on the _same/ opposite_ side of the mirror as the incident and reflected (outgoing) light.

2. For a mirror, the focal length is equal to __________ of the radius of curvature.

3. What is the image distance?

4. What is the image magnification?

5. The sign of the image distance is ___________________, so the image is _real/ virtual_ and is formed on the _same/ opposite_ mirror side as the object. The sign of the magnification is __________________, so the image is _upright/ inverted_. The magnification is _less than/ equal to/ greater than_ 1, so the image size is ______________________ than the object size.

A bullet is fired horizontally at a stationary 7.0 kg target. The target sits on a frictionless horizontal

surface and is connected to a spring on the backside of the target. The spring has a spring constant

of 5000 N/m. The 11.0 g bullet is traveling horizontally at 675 m/s the moment before it strikes

the target. After 1 ms, the bullet is embedded into the target and begins to oscillate. Ignore air

resistance.

(a) Determine the speed of the block immediately after the collision.

(b) Find the period and amplitude of the resulting simple harmonic motion.

(c) On separate graphs, plot the position vs. time, velocity vs. time, and acceleration vs. time for the system starting when the bullet is fully embedded into the target. Be sure to clearly label

your axes and the scale of each graph.

(d) On a single graph, plot the potential energy, kinetic energy, and total mechanical energy as a function of time for the system starting when the bullet is fully embedded into the target. Be sure to clearly label your axes and the scale of your graph.

3. (a) What is “photon bunching”? Draw a simple diagram.

(b) Explain which histories interfere and why assuming that the photons are indistinguishable.

(c) What is the final conclusion? What do the photons do?