Tagged Questions
0
votes
1answer
61 views
Vector cross product of $\mathbf{r}$ and $\ddot{\mathbf{r}}$ in polar coordinates
I'm struggling with the following question:
Question 6 A planet of mass $m$ moves under the gravitational attraction of a central star of mass $M$. The equation of motion of the planet is
...
0
votes
1answer
66 views
How is torque equal to moment of inertia times angular acceleration divided by g?
How is the following relation true
$$\tau = \large\frac{I}{g} \times \alpha$$
where $\tau$ is torque,
$I$ is moment of inertia,
$g= 9.8ms^{-2}$,
and $\alpha=$ angular acceleration.
0
votes
1answer
39 views
Calculating the moment inertia for a circle with a point mass on its perimeter
I want to calculate the tensor of the moment of inertia. Consider this situation:
The dot represents a points mass, in size equal to $\frac{5}{4}m$. $m$ is the mass of the homogenous circle. I'm ...
0
votes
1answer
59 views
A sphere rolling down a rough wedge which lying on a smooth surface
A sphere of mass $m$ and radius $r$ rolls down from rest on an inclined (making an angle $\phi$ with the horizontal ) and rough surface of a wedge of mass $M$ which stays on a smooth horizontal floor. ...
4
votes
2answers
326 views
Quantum Mechanics: Show that the expectation value of angular momentum does not change with time
The potential is given by $V\left(\left\|(x,y,z)\right\|\right)$, so $[\hat{L}, \hat{H}] = 0$.
Using the definition of $\langle \hat{L} \rangle$ and the time-dependent Schrödinger equation, show that ...
2
votes
0answers
137 views
How is parity relevant to determining angular momentum?
Question:
Particle A, whose spin $\mathbf{J}$ is less than 2, decays into two identical spin-1/2 particles of type B.
What are the allowed values of the orbital angular momentum $\mathbf{L}$, ...
3
votes
2answers
124 views
Space Quantization of Quantum Angular Momentum
I am trying to understand what my book is trying to convey.
Quantum angular momentum is $L_z = m_l \hbar$
"Choosing arbitrarily a z axis and using an appropriate experimental technique, we measure ...
2
votes
1answer
183 views
How can a satellite's speed decrease without its orbital angular momentum changing?
I have no idea what the answer is. I'm supposed to answer it within 3-4 sentences.
1
vote
1answer
46 views
Relationship between angular momentum of Earth and recession rate of the Moon
So the problem goes like this:
Two masses $m_1$ and $m_2$ orbit each other with semimajor axis $a$. The orbit is circular, and $m_1 \gg m_2$. The body $m_1$ has a rotational moment of intertia $I_1$ ...
0
votes
0answers
65 views
Help course exercises vol.1 Cap Berkeley. 6 [closed]
1 2. Angular momentum of tetherball. The object of the game
tetherball (Fig. 6.24) is to hit the ball hard enough and fast
enough to wind its tether cord in one direction about the
vertical post to ...
1
vote
1answer
321 views
Poisson brackets and angular momentum
I'm trying to find $[M_i, M_j]$ Poisson brackets.
$$\{M_i, M_j\}=\sum_l \left(\frac{\partial M_i}{\partial q_l}\frac{\partial M_j}{\partial p_l}-\frac{\partial M_i}{\partial p_l}\frac{\partial ...
1
vote
0answers
35 views
Calculate Rotational Intertia
If a can of soup, and a can of beans (tightly packed), are set in a race down a rough hill (has friction), the soup wins, because the inside of the can (soup) is not drawing energy from the system.
...
0
votes
1answer
115 views
What is the meaning of change of angular momentum of a ballistic object during its flight?
In a 2D world, three stones, whose magnitude of initial velocities are 5000m/s, are thrown from the North pole towards the Equator with horizontal initial angles of 15o, 30o, 45o and 60o angles. Their ...
-1
votes
1answer
83 views
Implications of rotational invariance
The state
$$|\psi\rangle ={1\over \sqrt 2}(|+\rangle|-\rangle-|-\rangle|+\rangle)$$
of system made up of 2 spin-$1\over 2$ particles is invariant under the operator
$$\exp{i\theta S_y}.$$
What ...
2
votes
0answers
121 views
Angular momentum confusion
Could somebody please explain what is going on here?
We have a system of two indistinguishable spin-1 bosons. We shall adopt the center of mass frame.
Let
$S$ = total spin
$L$ = relative orbital ...
1
vote
2answers
276 views
Tensor product decomposition of SU(2)
I have a rather trivial question. I am looking for the decomposition of $1/2\otimes 1/2\otimes 1/2$. It should give, $0,1/2$ and $3/2$. I thought one must get as the overall dimension of this space 8, ...
0
votes
0answers
815 views
Moment of Inertia problem [closed]
I'm revising for my exam and there's this one problem where I can't get the correct answer, so I'd like to know how to solve it. The problem is:
Two boys, each with a mass of 30kg, are sitting ...
0
votes
1answer
170 views
Angular momentum conservation in a central field through the Hamiltonian
In my teacher's notes there is a discussion of the Hamiltonian for a central force field with potential $V(r)$.
The Hamiltonian is formulated in spherical polar coordinates:
...
2
votes
3answers
815 views
Proving angular momentum is conserved for a particle moving in a central force field $\vec F =\phi(r) \vec r$
A problem I am trying to work out is as follows:
A particle moves in a force field given by
$\vec F =\phi(r) \vec r$. Prove that the angular momentum of the particle about the origin is constant.
...
0
votes
1answer
84 views
Period of an Object in Periodic Motion
My attempt (if it matters):
The initial period is given by $T_X = \frac{2\pi X}{v}$ for some $v$.
The new period is given by $T_Y = \frac{2\pi Y}{v}$ for the same $v$.
$Y = \frac{X}{2}$, so ...
2
votes
3answers
1k views
Angular momentum equations
I do not understand this because angular momentum is $L=I\omega$ ($I$ is moment of inertia;$\omega$ is angular velocity) but it I have also seen equations where $L= rmv\sin(x)$. I do not understand ...
0
votes
1answer
559 views
Derivation of angular momentum commutator relations
I'm trying to understand the derivation of the angular momentum commutator relations. How is
$$[zp_y, zp_x] ~=~ 0?$$
How is
$$[yp_z, zp_x] ~=~ y[p_z, z]p_x?$$
3
votes
1answer
523 views
Angular momentum coupling-calculation of Clebsch–Gordan coefficients
I am facing problem in calculating the value of given Clebsch–Gordan coefficients representing the coupled angular momenta of two-particle system. For example
$$\begin{pmatrix}2 & 1 & 2 \\ 1 ...
3
votes
1answer
485 views
Conservation of angular momentum for a nonrigid body
Question:
The sun is not a rigid body but a hot ball of gas. The period of rotation varies from 37 days at the pole to 26 days at the equator. The mean radius of the sun is $7\times 10^8\text{ ...
2
votes
2answers
378 views
Homework about spinning top
I have a top of unknown mass that has a moment of inertia $I=4\times 10^{-7} kg \cdot m^2$. A string is wrapped around the top and pulls it so that its tension is kept at 5.57 N for a distance of .8 ...
0
votes
3answers
3k views
Period of Precession
I'm trying to find the period of precession for a gyroscope. Now I was able to find the angular precession rate, which was 1.132 rad/s, but I have no idea how to convert this to a 'period', and google ...
1
vote
2answers
266 views
Angular Momentum and Force
I'm stuck on number 5. The answers to the first 4 are correct, but I dont know how to set up number 5. Any idea that I would have would require me having some kind of time information, but thats not ...
1
vote
2answers
1k views
Angular Momentum and Average Torque
Refer to number 6. This is the one I'm stuck on. So angular momentum is conserved right, so initial angular momentum is equal to final angular momentum. Initial is 7.87 so final must be 7.87, right? ...
