A rotating wheel obeys the equation theta(t)= 8.9t-14.0t^2+1.84t^4 where theta is in radians and t is in seconds.

What is ω at t = 4.0 s? Use 'rad/s' for your units.

What is α at t = 4.0 s? Use 'rad/s^2' for your units.

What is the average angular velocity between t = 1.0 s and 2.0 s? Use 'rad/s' for your units.

What is the average angular acceleration between t = 1.0 s and 2.0 s? Use 'rad/s^2' for your units.

Many techniques exist to measure the surface energy between a liquid and a liquid or a liquid and a gas (see e.g. the wiki page).

Methods to measure the surface energy between a solid and a fluid are rare, but still there is a method developed by Zisman (see e.g. here) that allows you to at least estimate it by extrapolation for solid/gas or solid/liquid, depending on the environment that you use in your experiment

What I wonder: is there a method to measure the surface energy between two non-elastic solids?

One option I could think of is that you could melt one of the solids and then use the technique of Zisman, but this will limit your knowledge to high temperature surface energy, whereas the ones at low temperature are the thing you are typically interested in.

Plot the 3-Dimensional Radiation Pattern, Plot of Azimuth and Elevation radiation pattern of the Horn antenna. Simulate it for the 100 MHz? What is the Directivity of the antennas. What is the Beam-width and Sidelobe levels?

WHERE THE FOLLOWING COORDINATES ARE LOCATED

(60 ° W, 15 ° N)
(120⁰ W, 45⁰ N)
(30⁰ E, 30⁰ N)
(90⁰E, 30⁰ N)
(90⁰ W, 30⁰ N)
(120⁰ W, 45⁰ S)
-Which are on the same meridian

Which are the same length.

Which have the same latitude.

Which see the same constellations at different times.

Which see different constellations at the same time.

A flat surface of dimensions 2 m by 2 m that is given a total charge of 400 μC uniformly distributed over the surface, and where a point charge +4 μC is fixed a distance 2 cm above the centre of the charged surface. A second point charge +16 nC, with mass 10 g, is placed at rest directly above the first point charge, at a distance 2 cm from the first point charge. The second point charge is released and accelerates directly away from the first point charge and charged surface. After some time, the second point charge is a distance 3.4 cm from the first point charge. What is the speed of the second point charge at this time?

Rotate the stage slightly such that the incident angle is just below the critical angle. Which color appears first. Why is this? How does the index of refraction depend on the wavelength of light?

The coordinates of two spacetime events are given by (ct1, x1) = (2, 5) and (ct2, x2) = (3, 3) in an inertial reference frame K.

a) Calculate the squared spacetime interval between these events. Is their spacetime separation spacelike or timelike? (

b) Transform the co-ordinates of this pair of events to a new reference frame, K0 moving relative to the one used in (a) with a constant speed u = −2 × 108m/s in the x direction. Explicitly show that the squared spacetime interval between the events is the same in the new reference frame.

(c) Compare the time ordering of events in the two reference frames – you should find that the ordering has changed. In general such a change of ordering would lead to causal paradoxes, for example: the girl calls her dog, the dog obeys; versus, the dog obeys, the girl calls her dog. Explain (with the aid of a spacetime diagram) why this is not a problem in the case of the events analysed in this question

What is the difference between a magnetic dipole and a magnetic moment?

Conducting research within 500 words on one of the following topics

mechanics
electricity
physics and applications of light
heat and properties of matter

Consider a system of ? point particles obeying quantum mechanics constrained to move in a two-dimensional plane (1 2-D ideal quantum gas) in a microcanonical ensemble. Find a formula for the entropy ? via Ω, the number of microstates with energy ≤ ? and show that it is an extensive property of the system.

Observations of a galaxy located 20 Mpc away give us the total flux and the radial velocity of stars within circles on the sky that correspond to radii of 100 and 1000 pc.

Within these two regions, the results are as follows:

100 pc radius -- Total flux (W m^-2):  2.1×10^-16,  v_r (km s^-1): 290

1000 pc radius -- Total flux (W m^-2): 1.5×10^-14,  v_r (km s^-1): 250

Use these data to answer the following questions about the galaxy.

A) Calculate M, L, and M/L, all in solar units, for the region of the galaxy contained within a 1 kpc radius.

B) Repeat for a 100 pc radius.

C) Based on your answers for the first two parts, do you think there is a supermassive black hole at the center of this galaxy? Estimate the mass of the possible black hole.

A mass m=4 is attached to both a spring with spring constant k=145 and a dash-pot with damping constant c=4.

The ball is started in motion with initial position x₀=1 and initial velocity v₀=6 .
Determine the position function x(t) .

x(t)=?

Note that, in this problem, the motion of the spring is underdamped, therefore the solution can be written in the form x(t)=c₁e^(-ρt)cos(ω₁t-α₁) . Determine c₁, ω₁, ρ and α₁.

c₁=?
ω₁=?

ρ=?

α₁=?

Graph the function x(t) together with the "amplitude envelope" curves x=-c₁e^(-ρt) and x=c₁e^(-ρt).

Now assume the mass is set in motion with the same initial position and velocity, but with the dashpot disconnected ( so c=0). Solve the resulting differential equation to find the position function u(t).
In this case the position function u(t) can be written as u(t)=c₀cos(ω₀t-α₀). Determine c₀, ω₀,and α₀.

c₀=?
ω₀=?

α₀=?

-After observing all energy demonstrations listed below, write a preliminary working definition of energy.

The energy demonstrations are:

1. beaker of water brought to boil over a hot plate or stove.
2. viscous heat pack (you have all seen them work, you do not have to buy one unless you do not know how they work.
3. popcorn to be popped and eaten (great with your loved one and a movie).
4. battery operated or windup toy car set into motion.
5. children's blocks stacked so that the top block balances precariously.
6. spring-loaded mouse trap (don't get your fingers caught).
7. operating a light bulb
8. walk up and down a flight of stairs a few times (no heart attacks please)
9. turn on a hair dryer.

3. An 8 kg stone rests on a vertical spring of force constant 785 N / m. The stone is pushed down about 30 cm and released. (a) Obtain the elastic potential energy of the compressed spring just before releasing it (b) Obtain the maximum height reached by the stone (c) Obtain the velocity just after it leaves the spring.

A high tech company operates a satellite which can measure the size of features on the surface of the earth. They use this technology to measure a particular rectangular field and find it's length to be 615 ± 1.78 (in meters) and it's width to be 170 ± 1.27 (in meters). They plan to report the area of the field as A±ΔA in units of acres. (1 acre = 4840 square yards & 1 meter = 1.094 yards) What is ΔA?