Rotational Definition and 1000 Threads

Homework Statement Let’s have one box, one pulley, and one rolling cylinder. Each of them have mass M, the pulley’s radius is R, and the cylinder’s radius is 2R. Consider the cylinder to be rotating about its center of mass. (a) Draw correct and complete free-body diagrams. (b) Give the...

General Relativity... Non-rotational spherically symmetric body of isotropic perfect fluid Einstein tensor metric element functions: g_{\mu \nu} = \left( \begin{array}{ccccc} \; & dt & dr & d \theta & d\phi \\ dt & g_{tt} & 0 & 0 & 0 \\ dr & 0 & g_{rr} & 0 & 0 \\ d\theta & 0 & 0 & g_{\theta...

I can't get it why tension is different in both sides of pulley due to friction?

Homework Statement A 60.0-kg grindstone is a solid disk 0.550m in diameter. You press an ax down on the rim with a normal force of 140N(Figure 1) . The coefficient of kinetic friction between the blade and the stone is 0.60, and there is a constant friction torque of 6.50N⋅m between the axle of...

Would there be any way to get the energy from the rotation of a planet, which is an Earth like planet in material, sized like Jupiter, and seems to have a 24 hr day. I am just starting to get into real Physics, So I am not even sure where to start getting the numbers to work with, and I would...

Hey PF readers, I am currently in dire need of a good(awesome) book on rotational and/or rolling motion which explains ALL the concepts and nicks of rolling and rotational motion. The book need not have many questions to practice bit should have HUGE amount of theory, that is, concept. It would...

Homework Statement A torque acts on a wheel rotating at 19.8 rad/s and increases its angular speed to 23.5 rad/s in 11.2 s. Find the angle through which the wheel turns during this time. Homework Equations omega = theta/time The Attempt at a Solution 23.5 - 19.8/11.2 = .33rad/s/s --- this is...

Homework Statement http://imgur.com/eYoa8Ut Homework Equations Torque=rt=I(alpha) t-mg=-ma alpha = a/r The Attempt at a Solution t-mg=-ma is the equation for the hanging mass. To find how much this turns the small wheel, rt=I(alpha) I and r are known rt=Ia/r I'm not sure what to do from...

There is an experimental set up that looks like the attitude file. 1) for mass hanging down the pulley write Newton's second law 2)since the sensor measures α find substitute a with a variable containing α 3) for the drum (horizontal pulley) find another equation for torque other than τ = Iα 4)...

Homework Statement I'm given the following four structures with their rotational axes marked, I have to rank them from largest to smallest rotational inertias, I have trouble with that apparently. Homework Equations No equations are really necessary, just my book says the more mass there is...

I think I'm not understanding some conceptual part of rotational kinematics because all the questions seem connected. I want to figure it out as best I can so please don't solve it but any hints in the right direction would be really appreciated, thanks! The Question: A stiff piece of wire is...

Hello Forum, If a net nonzero torque is applied to an object that is able to rotate, the object will spin at an increasing angular speed. The torque causes angular acceleration. In the case of a car engine, the engine eventually spins at a max constant rotational speed omega. Why does the...

In what way does mechanical efficiency in gears affect output torque and angular velocity? Mechanical efficiency affects power which is the product of torque and angular velocity. Let's say we have a gearbox with a mechanical efficiency of 0.95, hence the output power is 95% of the input power...

Hey there folks, As a forward: I'm trying to build a "high fantasy" universe in which to write stories, but within its historical timeline of events there are some cosmological happenings that I'd prefer to not just wave a wand at, so to speak. I'd like there to be at least SOME solid...

Homework Statement A motor imposes 5 Nm on a shaft of a 100kg flywheel which is 80cm(diameter) What is the rotational kinetic energy after 10 mins? assuming the flywheel was at rest and the mass moment of inertia of the shaft is negligble. Homework Equations Ig=1/2 * mr^2...

Homework Statement A wheel is spinning at n=1200rpm. The wheel starts to linearly decelerate, and after t=100s it stops. Determine the velocity, and acceleration of a point 10cm from the center of the mass, after 50 seconds of decelerating. The radius of the wheel is 30cm.Homework Equations...

Homework Statement How to derive W=(.5*I)*((ωf^2)-(ωi^2)) from W=τ*(θ) Homework Equations The two equations seen above (big W is work; little w is rotational velocity, τ is torque, alpha=rotational acceleration). s=r*θ a=r*(alpha) (ωf^2)-(ωo^2)=2*(alpha)*(θ) F=r*τ F=ma...

Why do we use inertia in rotational motion and not the whole mass of an object ?

I've attempted this problem several times and keep getting 14 rads as the answer but its not an available answer choice... any help would be greatly appreciated. The problem: A uniform rod (mass = 2.0 kg, length = 0.6 m) is free to rotate about a frictionless pivot at one end. The rod is...

Hello Forum, I am confused about the concept of rotational energy levels, electronic energy levels, and vibrational levels. A graph of "Energy versus Distance" is usually presented and the various horizontal bars represent the energy levels, which are simply energy amounts. The energy of...

Homework Statement Consider a solid disk of mass m and radius R rolling along a horizontal surface with the center of the disk moving horizontally with a speed v. The total kinetic energy of the disk is a combination of translational kinetic energy , KEt and rotational kinetic energy, KEr...

The question is the first part of Question 63. It is required to make a proof. What I was trying to do is to build a equation with Torque= Moment of Inertia * angular acceleration. But when it was simplified to 3g cos(sita)= r* dw/dt, it seems not easy to solve it, since both of sita and dw/dt...

Homework Statement The rotating drum on a clothes washer has a rotational inertia of 1.2 kg*m^2. In the spin cycle, it rotates at 240 rev/min. (a) What length of time is required for a 0.25 hp motor to bring the drum to this rotation rate starting form rest? (b) If the angular acceleration is...

Hi, I have a question I'd like some help with which is related to my job working with drill rigs. Where you have a cylinder such as a drill string where the forces of the ground pressing in from all sides how much influence does the surface area have on the rotational force required to...

Hi Everyone, I'm having some trouble with a problem concerning translational and rotational equilibrium. The question involves a balance with various masses suspended from it (see attached image). The question states that the counterweight is moved from 1cm away from the fulcrum to 2cm away from...

Hi. According to Griffiths the conmutation relations for the angular momentum and spin operators conmutation relations can be deduced from the rotational invariance, as in Ballentine 3.3. For the angular momentum seems logical that it is so, but how is it that rotational invariance leads to...

Homework Statement A small body A is fixed to the inside of a thin rigid hoop of radius R and mass equal to that of the body A. The hoop rolls without slipping over a horizontal plane; at the moments when the body A gets into the lower position, the center of the hoop moves with velocity v0...

Hello, I am having to find the rotational diffusion of a magnetic particle inside of water. I already have a diffusion coefficient but I do not know how to take into account the restoring force that the particle will feel from the magnetic field. The info that I know is: B-Field Strength...

Homework Statement A cylinder of mass M and radius R, with moment of inertia: I_c = \frac{1}{2}MR^2 rolls down without slipping through an inclined plane with an angle of θ, while pulling a block of mass Mb with an attached frame (of insignificant mass) which is connected to the axis of...

Homework Statement Determine the length of day on a planet. Imagine a planet with an acceleration at the equator of a_{equator} = 10 \,\, m/s^2 (ignoring rotation). Object dropped at equator falls with an acceleration of: a_{obj} = 9.7 \,\, m/s^2 , r = 6.2 \times 10^6 \,\, m ...

Homework Statement Two blocks of masses m1 = 8.00 kg and m2 = 12.00 kg are connected by a string of insignificant mass. The string lies on a cylinder of mass 0.50 kg and a radius of 0.15 m. The coefficient of kinetic friction between m1 and the surface of an inclined plane is 0.10. The angle...

So, I'm trying to study phase shift in an unbalanced rotating system (where "phase shift" means the resulting response of orbital motion lags behind in time/position relative to the force that's causing it) I know that conservation of angular momentum applies ideally in a closed system...

Homework Statement Starting from rest, ahollow ball rolls down a ramp inclined at angle θ to the horizontal. Find an expression for its speed after it's gone a distance d along the incline. Homework Equations I for sphere = 2/5*M*R^2 The Attempt at a Solution I know we have to use...

When thinking of a spherical shaped particle moving about under Brownian motion, one describes its motion by Diffusion. The units being \frac{m^2}{s} I can understand this physically as a distance it will travel from a certain point in space averaged over x-y and z direction. Now rotational...

Homework Statement A solid sphere of mass 6.0 kg is mounted on a vertical axis and can rotate freely without friction. A massless cord is wrapped around the middle of the sphere and passes over a 1.0 kg pulley and is attached to a block of mass 4.0kg. What is the speed of the block after it...

Homework Statement A light string is wrapped around a solid cylinder and a 300g mass hangs from the free end of the string. when released, the mass falls a distance of 54cm in 3.0s. a) Calculate the tension in the string. b) Calculate the mass of the cylinder. Homework Equations...

Homework Statement 15. A solid sphere of mass 6.0 kg is mounted on a vertical axis and can rotate freely without friction. A massless cord is wrapped around the middle of the sphere and passes over a 1.0 kg pulley and is attached to block of mass 4.0 kg, as shown. What is the speed of the...

Homework Statement A uniform solid sphere of radius R rolling on a rough horizontal surface without slipping, with an angular velocity 'w' meets a rough inclined plane of inclination 60degrees. The sphere continues to roll up the plane without slipping with an angular velocity 'n' given by...

Homework Statement A small solid disk (r<<R), mass m = 9.3 g, rolls on its edge without skidding on the track shown, which has a circular section with radius R = 9.7 cm. The initial height of the disk above the bottom of the track is h = 30.8 cm. When the ball reaches the top of the circular...

Hello everyone, I am trying to solve some homework but I am not entirely sure what formulas to use. Problem) There are 3 kids that weigh 25kg each sitting in the center of a merry go round (Disk). The merry-go-round weighs 400 kg and has a diameter of 3 m. It is initially spinning at 50 rpm...

Homework Statement An R-branch of a band of a ^1\Sigma - ^1\Sigma of CO has its maximum intensity at J'=11. The internuclear distance is 1.1 Ǻ. Estimate the rotational temperature. Homework Equations My notes don't even really define what rotational temperature is. They say that the...

Homework Statement The magnitude of the acceleration of a point on a spinning wheel is increased by a factor of 4 if: A) the magnitues of the angular velocity and the angular acceleration are each multiplied by a factor of 4 B) the magnitues of the angular velocity is multuplied by a factor...

Homework Statement Calculate the work done on a solid cylinder of mass 5.0 kg and radius 55.6 cm by an applied force of 12.2N if it turns 45 degrees. Homework Equations W = torque x angle (radians) The Attempt at a Solution I just used: W = torque x angle = Force x...

Hi From what I understand as the rotor yaws, there are gyroscopic forces that act upon it and the magnitude of these depends on the speed of yawing (e.g. 10 degrees per second). What happens to the rotor rotational speed during yawing? Does it slow down? Is the aim to slow down the rotor...

If I have say a stationary rod, and a particle collides with the rod whilst moving at speed v at the top end, why does the rod then proceed to rotate about the centre of mass of the system (whether that be in an elastic or completely inelastic collision where they both stick together). I...

Hi I am using Simple Harmonic Motion in a Matlab/Simulink model. Instead of using a motion for a simple pendulum, I decided to use a spring with a mass. The reasons for this is because my example is more like a lever attached to a pivot point and having an object at the end with a mass. A...

Homework Statement Energy is released by the Crab Nebula at a rate of about 5×10^31W, about 105 times the rate at which the sun radiates energy. The Crab Nebula obtains its energy from the rotational kinetic energy of a rapidly spinning neutron star at its center. This object rotates once...

Homework Statement A 2.8-m-diameter merry-go-round with rotational inertia 140kg⋅m2 is spinning freely at 0.40rev/s . Four 25-kg children sit suddenly on the edge of the merry-go-round. a) Find the new angular speed. b) Determine the total energy lost to friction between the children...

Homework Statement A gymnast with mass m1 = 46 kg is on a balance beam that sits on (but is not attached to) two supports. The beam has a mass m2 = 118 kg and length L = 5 m. Each support is 1/3 of the way from each end. Initially the gymnast stands at the left end of the beam. What is the...

Calculate the kinetic energies of two uniform solid cylinders, each rotating about its central axis. They have the same mass, 1.25 kg, and rotate with the same angular velocity, 235 rad/s, but the first has a radius of 0.18 m and the second a radius of 0.73 m. I got 12112188.868 for ω, and...