Rotational Definition and 1000 Threads

This is not a homework question. An adult exerts a horizontal force on a swing that is suspended by a rope of length L, holding it at an angle θ with the vertical. The child in the swing has a weight W and dimensions that are negligible compared to L. The weights of the rope and of the seat...

Homework Statement A quarry crane is used to lift massive rocks from a quarry pit. Consider the simplified model of such a crane shown in the figure. (Figure 1) The ends of two poles are anchored to the ground at the same point (point O). From this point, one pole rises vertically and the...

Hey guys, So, I'm kinda distraught over this problem because, by all accounts, I should be able to get the problem no sweat. However, it just hasn't been happening. If you could point out my flaw, I would truly appreciate it! In the problem, we are asked to find the magnitude of the...

Homework Statement Consider a sphere that is placed at a table. The coefficient of kinetic friction between the sphere and the table is μ. At time t = 0, the velocity of the center of mass of the sphere is Vo = 0, and the sphere is rotating with respect of the horizontal axis with angular...

Homework Statement Show that if a Hamiltonian H is invariant under all rotations, then the eigenstates of H are also eigenstates of L^{2} and they have a degeneracy of 2l+1. Homework Equations The professor told us to recall that J: \vec{L}=(L_x,L_y,L_z)...

A mine cage of mass 4 tonne is to be raised with an acceleration of 1.5m/s^2 using a hoist drum of 1.5m diameter. The drum’s mass is 750kg and its radius of gyration is 600mm.The effect of bearing friction is equivalent to a torque of 3kNm at the hoist drum. What isthe driving torque required...

Homework Statement A ball of clay of mass m travels with velocity v in a path tangent to a disk of radius R and mass M. The clay collides with the disk tangentially to its outer rim ( a totally inelastic collision) and the clay and disk begins to spin about the axis. a) What is the final...

Edit: Nevermind, solved it. Homework Statement A ceiling fan with 80 cm-diameter blades is turning at 60rpm . Suppose the fan coasts to a stop 25 s after being turned off. What is the speed of the tip of the blade 10 seconds after being turned off? Through how many revolutions does the fan...

I was thinking about the rotational kinetic energy of fluids the other day and I realized that I have a huge gap in my knowledge of physics. Why doesn't rigid body rotational kinetic energy (KE = 1/2*I*ω^2) not apply to fluids or deformable bodies (it should at least be proportional to that...

Hi PF! I've been working on a research problem involving fluid dynamics, and I'm currently looking at a "bathtub flow". This is where water is draining through a hole, and we have a vortex. In a paper I have found dealing with this flow, the velocity potential was written as: \psi = Alnr + B\phi...

Homework Statement If we shift the rotation axis from the center of mass of an object, with no change in the orientation of the axis, what happens to the rotational inertia of the object around the axis? Homework Equations Calculating the Rotational Inertia The Attempt at a Solution Does it...

Homework Statement An green hoop with mass mh = 2.6 kg and radius Rh = 0.12 m hangs from a string that goes over a blue solid disk pulley with mass md = 2.3 kg and radius Rd = 0.09 m. The other end of the string is attached to a massless axel through the center of an orange sphere on a flat...

First, energy of a disk: \int \frac{dm}{2}r^2 \omega^2 =\frac{\omega^2}{2}\int_0^R m\frac{2 \pi r dr}{\pi R^2}r^2 =\frac{m\omega^2}{ R^2}\int_0^R r^3 dr=\frac{m\omega^2 R^2}{4 } Which agrees with other sources. However, in the following lies my problem: The equation for a circle...

Hello! How do I calculate the maximum possible rotational speed of a thin walled hollow cylinder? In other words, at what rotational speed will it explode due to centripetal force? This picture shows the plane of rotation...

Homework Statement The ropes in the figure are each wrapped around a cylinder, and the two cylinders are fastened together. The smaller cylinder has a diameter of 10 cm and a mass of 5.0 kg; the larger cylinder has a diameter of 20 cm and a mass of 20 kg. What is the angular acceleration of...

I'm studying rotational dynamics and I've got a couple questions I can't answer. I want to describe de movement of the bodies in the cases below, the coefficient of friction in all the cases is \mu . I will say what I think it would happen, and I would appreciate if you guys judge it right or...

Homework Statement The ropes in the figure are each wrapped around a cylinder, and the two cylinders are fastened together. The smaller cylinder has a diameter of 10 cm and a mass of 5.0 kg; the larger cylinder has a diameter of 20 cm and a mass of 20 kg. What is the angular acceleration of...

Homework Statement Show \frac{d}{dt}\langle\bf{L}\rangle = \langle \bf{N} \rangle where \bf{N} = \bf{r}\times(-\nabla V) 2. Homework Equations . \frac{d}{dt}\langle A \rangle = \frac{i}{\hbar} \langle [H, A] \rangle The Attempt at a Solution I get to this point...

I was taught there was two types of inertia. The translational inertia and the rotational inertia. If in the Earth for example, that has a translational motion around the Sun, and a rotational motion around itself, all forces disappeared, it would follow an uniform rectilinear motion tangent to...

Hi, The question I have is not for a numerical answer but for clarification. Some of the questions involving torque/rotational equilibrium describe a person standing on a plank. I know that the gravitational force of the person on the plank needs to be considered for translational and...

My textbook says, "for an object rolling without slipping down an incline, the frictional force fs is less than or equal to its maximum value. fs < μsFn Why is that? What happen it's greater than?? When do we have static friction in rotational motion? (for rolling object) Then in an example...

1) 10. Four objects are placed at rest at the top of an inclined plane and allowed to roll without slipping to the bottom in the absence of rolling resistance and air resistance. • Object A is a solid brass ball of diameter d. • Object B is a solid brass ball of diameter 2d. • Object C is a...

Two masses, 300 g and 400 g, are connected by a cord that passes over a pulley with a radius of 6.64 cm (an Atwood's machine). When released from rest, the 400-g mass falls 60 cm and the 300-g mass rises 60 cm in 4.00 seconds. Find the rotational inertia of the pulley. Four 100-g ice cubes at...

Homework Statement (see attachment) Homework Equations The Attempt at a Solution Do I need to take torque about C here? Any help is appreciated, Thanks!

Homework Statement A hollow cylinder of internal radius r and external radius R and mass M is connected by a string to a weight m. What are the angular and linear acceleration of the cylinder? Assume that the cylinder is rolling without slipping. What is the acceleration of the weight and...

Homework Statement So I'm stuck on part (ii) where we have to solve the rotational energy levels. Problem: http://screencast.com/t/9rZStJdG3wJ The answer is ii) 0, 3.84 cm-1, 11.52 cm-1 Homework Equations Equations: http://screencast.com/t/ubFEheGBz The Attempt at a Solution...

Homework Statement This is a two part question I can do about half of each but get a little lost when trying to finish. I have written all the values below but just in case the full question is here (sorry about clarity) - http://screencast.com/t/jHQTMFnYOhp λ = 308nm T = 2000K population...

Homework Statement I am making a hanging mobile which needs to be done mathematically by calculating torque. The problem is, I can't seem to figure out how to solve for the distance. You see, all of the problems we did in class talked about finding mass, but to do this project, I already...

Hi, Doing a quick scan of wikipedia, a radius of 22m going at 10 RPM would produce 1g in gravity on the edge. However, wouldn't other forces of the spin, torque and angular momentum, create huge problems? Intuitively, if I hold a spinning bicycle wheel, it is highly unstable and the...

Homework Statement A vacuum cleaner belt is looped over a shaft of radius 0.45 cm and a wheel of radius 1.80 cm. The arrangement of the belt, shaft, and wheel is similar to that of the chain and sprockets in Fig. Q9.4. (Just like a bicycle).The motor turns the shaft at 60 rev/s, and the...

Suppose a mass attached to a rope which winds around a rim or a disk. If the mass attached to the string falls x meters, should the string also move thorugh x meters around the rim or the disk which we can relate by s = r theta?

In rotational motion what is the difference between angular acceleration, radial acceleration and tangential acceleration?? ... Now suppose a rotating disk about its center (axis) rotating and a mass attached to the string of the rotating disk. By what v does it move... Is it just like v-rW...

Hi guys, if a particle that is rotating around a axis at a constant angular acceleration, and at the highest point, it broke loose and flies off tangently and horizontally into the air, does it have a tangential acceleration of r*angular acceleration alpha? Please help! This is found in...

Homework Statement If Inga, the Laboratory Assistant, rolls a spare head down a 4 m ramp because it was spherical and solid and too heavy at 4.5 kg at a speed of 4.5 m/s, what was its total kinetic energy? Homework Equations KE = (1/2) I ω^2 I = (2/5) MR^2 The Attempt at a Solution...

Homework Statement A uniform rod of mass m and length l is pivoted at point O. The rod is initially in vertical position and touching a block of mass M which is at rest on a horizontal surface. The rod is given a slight jerk and it starts rotating about point O. This causes the block to...

When you open a door you apply force in any particular direction and as a result you get rotational motion of the door. My question is how linear momentum is conserved in this case as linear momentum seems to have generated rotational motion? To clarify my question further, if we fix a rod from...

The puzzle is: "The figure below represents a small, flat puck with mass m = 2.24 kg sliding on a frictionless, horizontal surface. It is held in a circular orbit about a fixed axis by a rod with negligible mass and length R = 1.03 m, pivoted at one end. Initially, the puck has a speed of v =...

Hello, I was curious to know if there was some intuitive out-look on why rotational inertia depends on the distance of the mass from the axis of rotation; and why is this distance have to be squared?

Hello, Of the different rotational quantities of motion--angular velocity, angular acceleration, torque, angular momentum, etc.--, which of them has their direction perpendicular to the plane of rotation (not sure if I worded that correctly)? I am pretty certain that torque has its...

Homework Statement A barrel is lowered into a boat using the illustrated apparatus. The barrel can be considered to be a uniform cylinder with M=100kg and r=0.40m. The weight on the other end of the rope has m=30kg. Assume that the barrel does not slip against the wall, that the other 2...

Hi there, I've got a conceptual question about the normal force as applied to rotational motion. Suppose you have an object like a uniform disk. If the disk were set up so that its axis of rotation were about its centre of mass, it would just sit there and the normal force would be equal to...

I am right now studying Rigid Body dynamics.. I have some doubts regarding Dynamics... 1) When a body is rotating as well as translating...we say that every particle of the ..lets say ROD is moving with a resultant velocity = Vcm ( translational velocity of COM) + ω.R (where R is the...

Hi friends, Here is a typical problem https://fbcdn-sphotos-d-a.akamaihd.net/hphotos-ak-ash4/432331_2639240957573_1038427614_n.jpg It is an elastic collision. Here I am applying simply the conservation of linear momentum as, Momentum before collision = Momentum after collision i.e...

Hi friends the problem states like this: https://fbcdn-sphotos-f-a.akamaihd.net/hphotos-ak-ash3/s480x480/68815_2639239357533_424911713_n.jpg When the attached block is horizontal it is applying torque on the ring. Here I am using the formula T = Iα So, mg. r = (mr2(ring) +...

Hi Friends I am getting some problem in solving this question every time with the help of energy conservation. Please help me out. Here is the question https://fbcdn-sphotos-h-a.akamaihd.net/hphotos-ak-prn1/s480x480/32407_2637149505288_842292859_n.jpg Well I am doing that thing , By...

Hi friend I am really getting big problem in solving this question which is related to Rotational dynamics. Please help me in solving this. I will be heartily thankful to u all guys. The question is as follows ...

The problem I am working on is: "Big Ben, the Parliament tower clock in London, has an hour hand 2.70 m long with a mass of 300 kg, and a minute hand 4.20 m long with a mass of 100 kg (see figure below). Calculate the total rotational kinetic energy of the two hands about the axis of rotation...

The total kinetic energy (as viewed from one inertial frame) of a free, rigid body is the sum of all the infinitesimal kinetic energies of the components that comprise the body. How do we prove that for a rotating body E_k=\frac{1}{2}\left(M_{T} v_{c}^{2} + I_{c} ω^{2}\right)

I was thinking about using a power drill to spin up a gyro. Let's say this gyro has two segments, a wide center and narrow ends. And its a perfectly rigid body. When the power drill is placed at the wide part, more torque is applied to the gyro and the gyro's angular acceleration is...

Hi, I'm new to the forum, starting off with some rotational stuff that I am not grasping well... I have diagrams for each question too, which i feel are vital to understanding the questions Homework Statement A spherical ball bearing 0.025m in diameter, rolls without slipping down an...