Consider a sphere centered at the origin of radius 1 that
rotates about the z-axis in a "west to east" direction with
constant angular speed 
(t)cos(nt)cos(wt), cos nt)sin(t), sin(nt))
a(t)(t) ac(t) a(t)
10 (t)--(w2 + η2)cos(yt)
Homework Answers
Add Answer to:
Consider a sphere centered at the origin of radius 1 that rotates about the z-axis in a "west to ...
(a) A sphere with radius R rotates with constant angular velocity . A uniform charge distribution...
(a) A sphere with radius R rotates with constant angular velocity . A uniform charge distribution is fixed on the surface. The total charge is q. Calculate the current density in this scenario where . Show how the E-field is calculated using Gauss' Law and the direction (in spherical coordinates) of the current density. We were unable to transcribe this imageWe were unable to transcribe this image7 =
Consider the initial value problem below has a series solution centered at zero of y =...
Consider the initial value problem below has a series solution
centered at zero of y =
(x). Determine
'(0),
''(0) and
4(0).
y''+ x2y'+ cos(x)y = 0, y(0) = 2, y'(0) = 3.
We were unable to transcribe this imageWe were unable to transcribe this imageWe were unable to transcribe this imageWe were unable to transcribe this image
A hollow sphere of radius a has uniform surface charge density σ and is centered at...
A hollow sphere of radius a has uniform
surface charge density σ and is centered at the origin. It
sits inside a bigger sphere, also centered at the origin, with
radius b > a and uniform
surface charge density −σ. Because of the spherical
symmetry, the electric field will have the form () =
E(r) r̂, where
negative E(r) corresponds to an
electric field pointing towards the origin, and positive
E(r) corresponds to a field
pointing away. What is E(r)...
3. Under the influence of a vector field a particle spirals on the surface of a unit sphere toward the (t)-t and ф(t)- uppermost pole. With its spherical angular positions parametrically defined by 2...
3. Under the influence of a vector field a particle spirals on the surface of a unit sphere toward the (t)-t and ф(t)- uppermost pole. With its spherical angular positions parametrically defined by 24t, the particle's path can be defined t€[3m/2.2n. r(t)-sin(θ(t)) cos(d(t)) ị t sin(θ(t)) sin(φ(t))J+cos(θ(t)) k, Compute the work done by the constant vector field F(,y,z) 1 k in moving the particle along this path We were unable to transcribe this image
3. Under the influence of a...
In the 3D Cartesian system the rotation matrix is around the z-axis is (a 2D rotation):...
In the 3D Cartesian system the rotation matrix is around the
z-axis is (a 2D rotation):
Where
is the angle to rotate. Then rotation from A to A' is can be
represented via matrix multiplications: [A'] = [R][A]
Such a rotation is useful to return a system solved in
simplified co-ordinates to it's original co-ordinate system,
returning to original meaning to the answer. A full 3D rotation is
simply a series of 2D rotations (with the appropriate matrices)
Question: If...
A solid cylindrical conducting shell of inner radius a = 4.9 cm and outer radius b = 6 cm has its axis aligned with the z-axis as shown. It carries a uniformly distributed current I2 = 5.8 A in the po...
A solid cylindrical conducting shell of inner radius a = 4.9 cm
and outer radius b = 6 cm has its axis aligned with the z-axis as
shown. It carries a uniformly distributed current I2 =
5.8 A in the positive z-direction. An inifinte conducting wire is
located along the z-axis and carries a current I1 = 3.8
A in the negative z-direction.
1. What is By(T), the y-component of the magnetic
field at point T, located at (x,y) =...
3) A pendulum consists of a solid spherical mass of mass 3m and radius R whose...
3) A pendulum consists of a solid spherical mass of mass 3m and radius R whose center is attached to the end of a uniform rod of mass m and length 4R which is pivoted about an axis at its end. a) The pendulum is constructed with a sphere of mass 1.5 kg and radius 15 cm, rod of mass .50 kg and length 60 cm. The mass swings in simple harmonic motion of maximum amplitude of /6 radians. Find...
1 Moment of inertia of a solid uniform sphere around its axis of symmetry a) What...
1 Moment of inertia of a solid uniform sphere around its axis of symmetry a) What is the volume element dV of a sphere? b) Assume a constant density p MIV, calculate the moment of inertia, remember that r is measured from the rotation axis for each volume element Use the volume of a sphere to get a solution that only depends on the mass M and radius R of the sphere. c) 2) Spinning DVD On a DVD, data...
Where And Exercise 6.5.28 Let S (z, y, z) e R3 1 z? + уг +...
Where
And
Exercise 6.5.28 Let S (z, y, z) e R3 1 z? + уг + z2-1,#2 0} be the upper hemisphere of the unit sphere in R3. For each of the following integrals, first predict what the integral will be, and then do the computation to verify your prediction 22. 222. 1U. JS Definition 6.5.9 Let S,T C(RT, R). The wedge product of S and T is the alternating bilinear form SAT : Rn × Rn → R given...
(1 point) A body of mass 10 kg moves in the xy-plane in a counterclockwise circular path of radius 3 meters centered at the origin, making one revolution every 11 seconds. At the time t 0, the b...
(1 point) A body of mass 10 kg moves in the xy-plane in a counterclockwise circular path of radius 3 meters centered at the origin, making one revolution every 11 seconds. At the time t 0, the body is at the rightmost point of the circle. A. Compute the centripetal force acting on the body at time t. B. Compute the magnitude of that force. HINT. Start with finding the angular velocity o [rad/s] of the body (the rate of...
Consider the initial value problem below has a series solution
centered at zero of y =
(x). Determine
'(0),
''(0) and
4(0).
y''+ x2y'+ cos(x)y = 0, y(0) = 2, y'(0) = 3.
We were unable to transcribe this imageWe were unable to transcribe this imageWe were unable to transcribe this imageWe were unable to transcribe this image
A hollow sphere of radius a has uniform
surface charge density σ and is centered at the origin. It
sits inside a bigger sphere, also centered at the origin, with
radius b > a and uniform
surface charge density −σ. Because of the spherical
symmetry, the electric field will have the form () =
E(r) r̂, where
negative E(r) corresponds to an
electric field pointing towards the origin, and positive
E(r) corresponds to a field
pointing away. What is E(r)...
3. Under the influence of a vector field a particle spirals on the surface of a unit sphere toward the (t)-t and ф(t)- uppermost pole. With its spherical angular positions parametrically defined by 24t, the particle's path can be defined t€[3m/2.2n. r(t)-sin(θ(t)) cos(d(t)) ị t sin(θ(t)) sin(φ(t))J+cos(θ(t)) k, Compute the work done by the constant vector field F(,y,z) 1 k in moving the particle along this path We were unable to transcribe this image
3. Under the influence of a...
In the 3D Cartesian system the rotation matrix is around the
z-axis is (a 2D rotation):
Where
is the angle to rotate. Then rotation from A to A' is can be
represented via matrix multiplications: [A'] = [R][A]
Such a rotation is useful to return a system solved in
simplified co-ordinates to it's original co-ordinate system,
returning to original meaning to the answer. A full 3D rotation is
simply a series of 2D rotations (with the appropriate matrices)
Question: If...
A solid cylindrical conducting shell of inner radius a = 4.9 cm
and outer radius b = 6 cm has its axis aligned with the z-axis as
shown. It carries a uniformly distributed current I2 =
5.8 A in the positive z-direction. An inifinte conducting wire is
located along the z-axis and carries a current I1 = 3.8
A in the negative z-direction.
1. What is By(T), the y-component of the magnetic
field at point T, located at (x,y) =...
3) A pendulum consists of a solid spherical mass of mass 3m and radius R whose center is attached to the end of a uniform rod of mass m and length 4R which is pivoted about an axis at its end. a) The pendulum is constructed with a sphere of mass 1.5 kg and radius 15 cm, rod of mass .50 kg and length 60 cm. The mass swings in simple harmonic motion of maximum amplitude of /6 radians. Find...
1 Moment of inertia of a solid uniform sphere around its axis of symmetry a) What is the volume element dV of a sphere? b) Assume a constant density p MIV, calculate the moment of inertia, remember that r is measured from the rotation axis for each volume element Use the volume of a sphere to get a solution that only depends on the mass M and radius R of the sphere. c) 2) Spinning DVD On a DVD, data...
Where
And
Exercise 6.5.28 Let S (z, y, z) e R3 1 z? + уг + z2-1,#2 0} be the upper hemisphere of the unit sphere in R3. For each of the following integrals, first predict what the integral will be, and then do the computation to verify your prediction 22. 222. 1U. JS Definition 6.5.9 Let S,T C(RT, R). The wedge product of S and T is the alternating bilinear form SAT : Rn × Rn → R given...
(1 point) A body of mass 10 kg moves in the xy-plane in a counterclockwise circular path of radius 3 meters centered at the origin, making one revolution every 11 seconds. At the time t 0, the body is at the rightmost point of the circle. A. Compute the centripetal force acting on the body at time t. B. Compute the magnitude of that force. HINT. Start with finding the angular velocity o [rad/s] of the body (the rate of...
Most questions answered within 3 hours.
-
1. When a nearsighted person looks at an object that is in the
distance with their...
asked 36 minutes ago -
QUESTION 8
Both of these statements will store the same value in the
variable $number
$number...
asked 1 hour ago -
The price of 1 lb of potatoes is $1.75. If all the potatoes sold
today at...
asked 1 hour ago -
Garcia Company issues 20.00%, 15-year bonds with a par value of
$470,000 and semiannual interest payments....
asked 1 hour ago -
In C++ Programming, Try using loops only.
This lab demonstrates the use of the While Loop...
asked 2 hours ago -
Effect of DCMU and sodium azide on Chlamydomonas? We did an
experiment where we had Chlamydomonas...
asked 3 hours ago -
1a) According to the ideal gas law, _______________.
a. a gas has infinite volume at absolute...
asked 4 hours ago -
Oakdale Fashions, Inc. had $245,000 in 2018 taxable income.
Using the tax schedule in Table 2.3...
asked 5 hours ago -
The marketing class at CSUS had an average score of 150. An
educational analyst determined that...
asked 6 hours ago -
Justin Case has purchased a $250 000 home by putting 20 % down
and taking out...
asked 6 hours ago -
1. In a labor market, marginal cost for a firm is
____________.
a. recruiting cost
b....
asked 7 hours ago -
On January 1, 2019, ABC Company issued $60,000,000 of 20-year,
10.5% bonds when the market rate...
asked 7 hours ago