Angular Definition and 999 Threads

Hello all, I am having hard time to know if the finite angular displacement really a scalar quantity? In some books they say angular displacement when finite is Scalar and when infinitesimal small is Vector, with direction perpendicular to plane of circle government by right hand rule. I...

Homework Statement When the hand is rotating about the wrist in the sagittal plane its centre of mass has an acceleration of 3m/s(squared) in a horizontal direction, its mass is 2kg and the vertical direction (i.e. Y) is against gravity. The hand travels through 30 degrees. If the distance from...

One of the conditions to distinguish Simple Harmonic Motion from other harmonic motions is by the relation that a∝x where x is the displacement from the point that acceleration is directed towards But what confuses me is the constant of proportionality introduced to this relation: ω2 ω is...

Homework Statement For calculating angular frequency of a physical pendulum, I consider its center of mass motion. The COM motion is a simple pendulum motion. Considering a coordinate system whose origin is the pivot point. Then, the COM is the length of the corresponding simple pendulum. Is...

So the equation for angular acceleration on the AP physics sheet reads α = ΣT / I. I am required to prove that the units on each side are the same however I can't figure out how to get the rad/s^2 unit for angular acceleration into the same form as the right side which is N*m/ kgm^2 Any help...

Homework Statement Homework EquationsThe Attempt at a Solution Let's consider a cylindrical coordinate system whose z-axis coincides with the hinge and origin is the lowest point of the hinge. Let's say that the truck moves along the x-axis. W.r.t. this frame, Torque about the hinge ## \vec...

Homework Statement Homework EquationsThe Attempt at a Solution The angular momentum of the upper particle is given as ## \vec L_u = m \vec r \times ( \vec \omega \times \vec r )= m[ \vec \omega r^2 - \vec r ( \vec r . \vec \omega )] = m[ r^2 \vec \omega - \omega r \cos \alpha \vec r ]##...

Recently I was searching the internet and books for the connection between conservation of angular momentum and conservation of rotational energy and found nothing. Let's say an ice skater rotates and draws the arms in - the rotation speeds up. The rotational energy must increase because the...

Homework Statement A flywheel turns through 40 rev as it slows from an angular speed of 1.5 rad/s to a stop. (a) Assuming a constant angular acceleration, find the time for it to come to rest. (b) What is its angular acceleration? (c) How much time is required for it to complete the first 20 of...

Homework Statement Homework Equations Angular momentum = moment of inertia * angular velocity Change in angular momentum = impulsive moment v^2=u^2+2as The Attempt at a Solution First I used v^2=u^2+2as to find the velocity of the particle the moment the string goes taut. I got v=\sqrt{8ag}...

Homework Statement Homework EquationsThe Attempt at a Solution [/B] Since there is no net torque or net force acting on the system( which consists of the system given in the picture), I applied conservation of angular momentum and energy. I took on the L.H.S. the angular momentum or energy...

Homework Statement A pulley hangs of mass, m, and radius, R, hangs from the ceiling. Two blocks of masses, m1 and m2 are connected by a massless, non-stretchable rope on the pulley (assume no slipping). What is the angular acceleration of the pulley and what is the ratio of the tension forces...

I am sizing a linear actuator to build a BMX gate. Please see the drawing below. I have a metal gate that is 20" tall and 9.5' wide. It will be steel and weigh approximately 150lbs. I am mounting the rear of the linear actuator on a clevis 8" off the ground. The front will be mounted with...

If a rigid link pin joint-fixed on ground and is rotating freely about the same point with uniform ang. vel., can we say the vector form of angular vel. (omega) is nothing but moment of the tangential (perpendicular) vel. at the other end?

Homework Statement Homework EquationsThe Attempt at a Solution [/B] Initially the rod is in rotational equilibrium , so net torque about CM is zero . From torque equation about CM , we get Tension T in the left string = Force F (kx) in the spring Doing a force balance gives us T+F=Mg...

Homework Statement Note : In the above setup the string lengths are unequal and the left angle is 30° and right angle is 60° .Homework EquationsThe Attempt at a Solution [/B] Just after the string is cut , writing force eq. for rod in vertical direction . ##Mg - Tcos60° = Ma_y ## (1)...

Hello! I hope someone could help me to solve mu doubt, I am very confused and I don't find answers in internet. My question is about pendulums. I know the angular frecuency of a pendulum is give by the equation w= sqrt(g/L). But also i know the angular velocity (also named with "omega") can be...

Homework Statement A thin uniform rod (of mass 10.0 Kg and length of 1.20 m) is attached to a friction-free pivot. Initially, the rod is balanced vertically above the pivot (position A in the figure attached). If the rod falls from rest, calculate a. the angular acceleration at position B...

Let's assume that a disk is rotating with relativistic speed in a frame. We can find the velocity of a particle using v=rw formula. However, what is the r in this formula? is it the radius of the disk in rest frame or in the lab frame?? And Is the magnitude of velocity same for all points of...

Homework Statement A horizontal plywood disk with mass 6.90 kg and diameter 1.14 m pivots on frictionless bearings about a vertical axis through its center. You attach a circular model-railroad track of negligible mass and average diameter 1.04 m to the disk. A 1.40 −kg , battery-driven model...

Homework Statement A spherical asteroid with radius r = 123 m and mass M = 2.10×1010 kg rotates about an axis at four revolutions per day. A "tug" spaceship attaches itself to a vehicle which follows the asteroid's south pole (as defined by the axis of rotation) and fires its engine, applying a...

Homework Statement A 220-kg beam 2.8 m in length slides broadside down the ice with a speed of 23 m/s . A 68-kgman at rest grabs one end as it goes past and hangs on as both he and the beam go spinning down the ice. Assume frictionless motion. (Figure 1) Homework Equations L1=L2 Iω=L The...

Homework Statement Mod note: Fixed thread title. OOPS NOT Acceleration, Speed! (Thread title is incorrect) Homework Equations w=d∅/dt v=rw x={+,-√(b2-4ac)}/2aThe Attempt at a Solution I solved this with help from Chegg study, however, I'm still not entirely sure what I am doing. Obviously, for...

Considering the angular momentum of a collapsing star preventing it from resulting in a black hole by degeneracy pressure, are there ekpyrotic universe models that include angular momentum and degeneracy pressure as key factors of cosmic inflation?

What is time derivative of angular velocity ( measured w.r.t. an inertial frame ) of a rotating co. system w.r.t. the same rotating co. system? I think a person sitting in a closed rotating box feels the an object at rest w.r.t. him as rest. He doesn't observe the angular velocity of the...

Hello! Excuse my ignorance. The forum is full of difficult questions so I even feel a bit ashamed of posting this, But that is the only way I can learn. I do not understand some concepts stated below in the images, and I am not able to grasp what is being said. For instance, I do not know why...

Hi, Consider a spherical planet of mass m and radius rp orbiting a star with a circular orbit of radius ro (distance from axis of orbit to the planet's center of mass). The planet has an angular velocity ω. Say we wanted to find the magnitude of the angular momentum of the planet. Going about...

Homework Statement The 25-lb slender rod has a length of 6 ft. Using a collar of negligible mass, its end A is confined to move along the smooth circular bar of radius 32√ ft. End B rests on the floor, for which the coefficient of kinetic friction is μB = 0.24. The bar is released from rest...

Homework Statement The cylindrical container, when empty, has the moment of inertia of 2.0 Kgm^2 around the axis of rotation. It is rotating freely on its axis 20 revolutions per minute, when it begins to receive cereal, which falls vertically along its axis at the rate of 0.5 kg-1. The radius...

Homework Statement A solid sphere of radius 16cm and mass 10kg starts from rest and rolls without slipping a distance of 9m down a house roof that is inclined at 43 degrees. What is the angular speed about its center as it leaves the house roof? The height of the outside wall of the house is...

Homework Statement A horizontal plank with a frictionless axis of rotation at its center has a large mass at one end and a small mass at the other end. It is held stationary and then released from rest. As the plank rotates (and before one end hits the ground), the magnitude of the angular...

This is the problem I'm trying to understand: Consider two particles with spin 1 without orbital angular momentum. If they are distinguishable, from the rule of addition of angular momentum applied to spin, we'll have states of total spin j=0,1,2. If we have, however, identical particles which...

Homework Statement I have the following problem to solve: A 1.8m board is placed in a truck with one end resting against a block secured to the floor and the other one leaning against a vertical partition. The angle the Determine the maximum allowable acceleration of die truck if the board...

Homework Statement The Problem is the following: We have a uniform disk of radius r laying still with its center at the origin. Two bullets, with equal mass m and negligible size are approaching the disk, both with trajectories parallel to the x-axis and at distance h, -h from the y-axis...

I'm trying to understand the rotations of rigid diatomic molecules such as HCl. My understanding of the orbital angular momentum is that it is quantized with a total value equal to $$E=\frac{\hbar^2}{2I}J(J+1)$$ where I is the rotational moment of inertia and J is the quantum number. Also, J...

Homework Statement A constant torque is applied to a pinion which has a moment of inertia of I_m. The pinion(A) drives two gears, one (B) which is connected to a mass which has a moment of inertia = I_m and the other(C) is connected to a mass which has a moment of inertia = 2I_m. The gear...

Homework Statement Show that ##|l, m\rangle## for ##l=1## vanishes for the commutator ##[l_i^2, l_j^2]##. Homework Equations ##L^2 = l_1^2 + l_2^2 + l_3^2## and ##[l_i^2,L^2]=0## The Attempt at a Solution I managed to so far prove that ##[l_1^2, l_2^2] = [l_2^2, l_3^2] = [l_3^2, l_1^2]##. I...

The unit of angular momentum is kg * m^2 / s (or I * W). The moment of inertia for a point mass, mr^2's unit is kgm^2. That means the unit of W has to be 1/s. I'm having trouble converting this to radian/s. Thank you!

The question: A wheel was rotating at 12.5 rad/s when a torque was applied for 15.7 s. The angular velocity increased to 54.0 rad/s. What angle did the wheel turn through in that time? My Solution: theta = Wo*t+1/2*a*t^2 = (12.5 rad/s)(15.7)+(1/2)(41.5)(15.7)^2 therefore, theta =...

Homework Statement The directed beam from a small but powerful searchlight placed on the ground tracks a small plane flying horizontally at a fixed height h above the ground with a uniform velocity v. If the search light starts rotating with an instantaneous angular velocity ##\omega_0## at...

Homework Statement coefficient of kinetic friction between the disk and the surface is 0.42 gravity = 10.6 m/s disk mass = 1.75x10^9 the skid marks are 1280m long, This is due to the fact that uneven friction had set the saucer in very slow rotation around its principal axis. By...

There are two types of angular momentum: orbital and spin. If we define their operators as pseudo-vectors \vec{L} and \vec{S}, then we can also define the total angular momentum operator \vec{J} = \vec{L}+\vec{S}. Standard commutation relations will show that we can have simultaneous well...

1. Homework Statement Determine the total magnitude of angular momentum Ho of the particle about point O. The velocity of the particle is 5.5 m/s.Homework Equations Ho= r x mv The Attempt at a Solution The answer is 43.04. My question is, isn't the graph wrong? If you take the magnitude of the...

I am reading a proof of why \left[ \hat{L}_x, \hat{L}_y \right ] = i \hbar \hat{L}_z Given a wavefunction \psi, \hat{L}_x, \hat{L}_y \psi = \left( -i\hbar \right)^2 \left( y \frac{\partial}{\partial z} - z \frac {\partial}{\partial y} \right ) \left (z \frac{\partial \psi}{\partial x} -...

Hello I need help to explain the affect of the cross product without the its current symbolism, but for angular momentum. I can explain angular momentum in terms of the cross product of 3D space formulated like this: |r| |v| * sin(angler.v) e-perp to r and v Eq.1 (I can explain this to...

Homework Statement The red box only Homework EquationsThe Attempt at a Solution I suppose we have to show L_3 (Π_1) | E,m> = λ (Π_1) | E,m> and H (Π_1) | E,m> = μ (Π_1) | E,m> And I guess there is something to do with the formula given? But they are in x_1 direction so what did they have...

I've added a graph of coincidence events vs. detector angular separation. This is for a electron-positron annihilation (gamma-gamma coincidence) experiment. Why does the plot have a finite width and not look like a delta function? I'm assuming this is because the experimental conditions are...

Hi. I am revising my Mechanics: Dynamics by reading the Beer 10th edition textbook and Pytel 2nd edition In Pytel pg 358 art. 17.3 the angular momentum about the mass center of a rigid body in general motion is being calculated...

A spiral phase plate can change the orbital angular momentum of a beam of light. Should I think of the beam of light carrying the orbital angular momentum or the photons that make up the beam light? If the orbital angular momentum is carried by the individual photons what is being orbited, the...

Homework Statement A 39.00 kg rod of length 2.8 m is hanging vertically by one of its ends that is free to swing in a complete circle about a frictionless axle/pivot. The rod has uniform mass density. Suddenly it is struck horizontally by a 5 kg putty that sticks to the center of...