A cylinder with rotational inertia I₁ = 2.6 kg · m^2 rotates clockwise about a vertical axis through its center with angular speed ω₁ = 5.8 rad/s. A second cylinder with rotational inertia I₂ = 1.3 kg · m2 rotates counterclockwise about the same axis with angular speed ω₂ = 6.6 rad/s. If the cylinders couple so they have the same rotational axis, what is the angular speed of the combination (in rad/s)?

What percentage of the original kinetic energy is lost to friction?

1.12 [2pt] Consider one infinitely long straight wire with a uniform charge density of 1 C/m. Sketch the electric field around the wire

1.12 ANSWER

1.13 [2pt] In problem 1.12, calculate the magnitude of electric field at a distance R from the wire. How is it different (if any) from the field of a point charge?

1.13 ANSWER

1.14 [2pt] Consider two infinite wires 1 m apart with a uniform charge density per unit length 1 C/m. Calculate the force per unit length between the wires. To do this, just select a tiny, nearly point-like section of a wire of length Land calculate the force due to the electric field of the other wire using the Coulomb’s law. Your answer should be proportional to L. Divide it by L and this is the force per unit length.

1.14 ANSWER

1.15 [1pt] Explain, in a few sentences, how the electric force between two charged wires differs from the regular Coulomb law and why.

1.15 ANSWER

A short section of coaxial cable consists of a line current along the z-axis from z = -L to z = L carrying current ?0?̂ surrounded by a hollow cylindrical shell (centered on the z-axis, top at z = L , bottom at z = -L) carrying a surface current ?⃗⃗ = ?0 (−?̂). Radius R

a. Find an expression for the magnetic field at an arbitrary point (x, y, z)

b. Draw a qualitative graph of the magnetic field as a function of position on the x-axis.

A brine solution with a density of 1230 kg/m³ moves through a constricted pipe in steady, ideal flow. At the lower point shown in the figure below, the pressure is P₁ = 2.00 ✕ 10⁴ Pa, and the pipe diameter is 7.00 cm. At another point y = 0.40 m higher, the pressure is P₂ = 1.25 ✕ 10⁴ Pa and the pipe diameter is 3.50 cm.

(a) Find the speed of flow (in m/s) in the lower section.

(b) Find the speed of flow (in m/s) in the upper section.

(c) Find the volume flow rate (in m³/s) through the pipe.

In visible light, which color has the longest wavelength?'

Are Microwave, Visible Light, Gamma rays in order of lowest to highest energy?

are Radio broadcast, cell phone and GPS examples of technologies that uses radio waves

Each of the two identical springs in the figure below has force constant k = 1.16 103 N/m, d = 1.21 m, and θ = 29.0°. (a) Find the unstretched length of each spring. (b) Find the instantaneous acceleration of the weight if it is pulled 10.0 cm lower and released.

A charge of 3.77 μC is held fixed at the origin. A second charge of 3.45 μC is released from rest at the position (1.25 m, 0.570 m).

A.) If the mass of the second charge is 2.85 g , what is its speed when it moves infinitely far from the origin?

B.)At what distance from the origin does the second charge attain half the speed it will have at infinity?

The blood speed in a normal segment of a horizontal artery is 0.100 m/s. An abnormal segment of the artery is narrowed down by an arteriosclerotic plaque to 1/5 of its normal cross-sectional area. What is the difference in blood pressure between the normal and constricted segments of the artery?

An object with mass 0.190 kg is acted on by an elastic restoring force with force constant 10.3 N/m. The object is set into oscillation with an initial potential energy of 0.150 J and an initial kinetic energy of 6.90×10⁻² J.

A) What is the amplitude of oscillation?

Express your answer with the appropriate units.

A=

B) What is the potential energy when the displacement is one-half the amplitude?

Express your answer with the appropriate units.

U=

C) At what displacement are the kinetic and potential energies equal?

Express your answer with the appropriate units.

x=

D) What is the value of the phase angle ϕ if the initial velocity is positive and the initial displacement is negative?

Express your answer in radians.

phi =

1. In your own words, explain why Einstein's "greatest blunder" is no longer considered a blunder.

7. An inductor is designed to filter high frequency noise from power supplied to a personal computer. Do you connect the inductor in series or in parallel with the computer? Explain.

Please explained detailed step by step, with diagram.

In music, middle C has a frequency of about 256 Hz - the precise frequency depends on the tuning scheme. How does the wavelength of a middle C note propagating through air compare to the size of a typical human body? How does the wavelength of the same note propagating through water compare to the human body? What frequency of sound in air has a wavelength nearly the size of a human head? This size is important because we have diminished ability to determine the direction to a source of this tone.

A stick is resting on a concrete step with 2727 of its total length ?L hanging over the edge. A single ladybug lands on the end of the stick hanging over the edge, and the stick begins to tip. A moment later, a second, identical ladybug lands on the other end of the stick, which results in the stick coming momentarily to rest at ?=41.3∘θ=41.3∘ with respect to the horizontal, as shown in the figure.

If the mass of each bug is 3.093.09 times the mass of the stick and the stick is 16.3 cm16.3 cm long, what is the magnitude of the angular acceleration ?α of the stick at the instant shown?

At what distance on the axis of a current loop is the magnetic field half the strength of the field at the center of the loop? Give your answer as a multiple of R.

Express your answer in terms of R using two significant figures.