Rotational Definition and 1000 Threads

Homework Statement The Earth's radius is 6371 km. If the Earth's radius were to increase by 30 m (0.03 km), but no change in mass, by what percentage would the Earth's rotational period increase? (Model the Earth as a uniform sphere) Homework Equations ∑Torque = Iα v = rω a = rα KE = (1/2)Iω^2...

https://scontent-syd1-1.xx.fbcdn.net/hphotos-xfl1/v/t34.0-12/13015003_664975026975127_933044449_n.png?oh=0259712996d9a6dde812f6d8886f56b9&oe=5715CA95 So, it's straight forward enough to calculate the moment of inertia of basic planes with evenly distributed mass, but if I were to say glue the...

Homework Statement A solid sphere, starting from rest, rotates with constant angular acceleration α about a fixed axis passing through its center. Consider a particle within this sphere that lies at a perpendicular distance r from this axis. If, at some instant, the linear acceleration of this...

[Note: Post moved to homework forum by mentor] So I stumbled upon a reviewer for my physics exam tomorrow and I was wondering how the equation was formulated. Your help is very much appreciated :) ! Normally I would consult my professor for this but it's Sunday in my country today so I can't...

I am conducting an experiment that rotates a sealed donut cylinder to investigate amongst other things the inertia of the contained fluid. Process I rotate the cylinder to a set speed (assuming that the viscosity of the internal fluid will end up rotating the fluid to solid body rotation) then...

Homework Statement A disk roll without slipping down a incline plane. Identify the forces acting on the disk, explain qualitatively which of these forces do work. Homework Equations The rotational work is given by W=\int \tau_z d\theta (1) , where \tau_z is the component of the torque...

I have a doubt regarding the definition of rotational work, which is as follows W = \int \tau_z d \theta Where \tau_z is the component of the torque parallel to the axis of rotation z. My doubt concerns the fact that, looking at this definition, it seems that any torque which has an axial...

Homework Statement A bowling ball is released with speed V and no rotational kinetic energy. After a period of sliding and rotating, the ball enters pure rotational motion. The coefficient of friction between the ball and the ground while sliding is Uk. a. Show that the rotational acceleration...

Homework Statement A small gear with mass m and radius r rotate around a central axis. A force is applied to an interior hub at a radial distance r/2 from the axis. A. If a force of 4N is applied for 10s, what is the angular velocity of the small gear, assuming it starts at rest? B. Once it...

Homework Statement I am looking at part C.[/B] https://scontent-ord1-1.xx.fbcdn.net/hphotos-xal1/v/t34.0-12/12782422_10205657311624690_1648245885_n.jpg?oh=79b686a8b74392888fab0b070b86627d&oe=56F7E1E4 The Attempt at a Solution Here I am looking at part C. My initial thought is that they have...

Homework Statement A spool of thread consists of a cylinder of radius R1 = 6.6 cm with end caps of radius R2 = 9.3 cm as depicted in the end view shown in the figure below. The mass of the spool, including the thread, is m = 290 g. The spool is placed on a rough, horizontal surface so that it...

Homework Statement A wheel with rotational inertia I = 1/2MR^2 about its horizontal central axle is set spinning with initial angular speed omega_0. It is then lowered, and at the instant its edge touches the ground the speed of the axle is zero. Initially the wheel slips when it touches the...

Homework Statement Imagine a ball with moment of inertia I_{cm} = \beta MR^2 encountering a circular loop of radius R_0 > R after rolling on a level surface at a speed of v_0. Assume that the ball does not slip. Attached a diagram. A) What is the minimum value of v_0 required for the ball...

Homework Statement Rods of negligible mass connect discrete masses as shown in the diagram below. For each system, the masses rotate about the midpoint of each connecting rod. Furthermore the systems appear to rotate in unison as time progresses. Do the systems have the same velocity? Homework...

1. Homework Statement A cylinder of mass M and radius R rolls (without slipping) down an inclined plane whose incline angle with the horizontal is theta. Determine the acceleration of the cylinder's center of mass and the minimum coefficient of friction that will allow the cylinder to roll...

To show that the Lagrangian ##L## is invariant under a rotation of ##\theta##, it is common practice to show that it is invariant under a rotation of ##\delta\theta##, an infinitesimal angle, and then use the fact that a rotation of ##\theta## is a composite of many rotations of...

Homework Statement A major-League pitcher throws a baseball towards home plate. the ball rotates at 1560 rpms,and it travels 18.5 meters to the plate at an average translational speed of 40.2m/s.how many revolutions does the ball make during this trip? Homework EquationsThe Attempt at a...

I am having trouble wrapping my head around a physics concept. If we roll solid sphere down an inclined plane it will reach the bottom at a different time than if we were to say, roll a hoop down the same inclined plane. This is because they have different rotational inertias, and so more of...

Hi guys, I'm having a debate with a mechanical engineer friend of mine, and I was wondering if you could help me solve it. I'm not much of a physicist, but honestly I think he might have this one wrong, I just can't remember my old physics classes well enough to calculate and be sure. The...

Say you've got a dumbbell-type object sitting still in space, and a mass comes in from below and strikes it. We've got a collision. If the mass strikes the dumbbell away from the center of mass, then it will cause the dumbbell to do two things (1) rotate, (2) the center of mass will move up...

This isn't actually a homework problem, but I am still posting it here. I am confused by rotational inertia. How does mass distribution affect rotational inertia? Because I know it should, but I don't know how it would.

[Moderator's note: spun off from another thread.] How would Einstein calculate the rotational energy of a 6 kilometer long rigid bar with rest mass M rotating about its center with 15000 revolutions per second in gravity free space?

Homework Statement . What is the angular acceleration if a force of 3 N is applied perpendicular to the radius of a 5 kg solid sphere that has a radius of 0.6 meters? Homework Equations = r x F I = mr^2 The Attempt at a Solution I used tried solving for angular acce. 3N/(5kg)(0.6)...

Homework Statement I am trying to get the hamiltonain operator equality for a rigid rotor. But I don't get it. Please see the red text in the bottom for my direct problem. The rest is just the derivation I used from classical mechanics. Homework Equations By using algebra we obtain: By...

Homework Statement A solid sphere is set into motion on a rough horizontal surface with a linear speed v in the forward direction and angular speed v/r in the anticlockwise direction. Find the linear speed of the sphere when: a) When it stops rotating b) when slipping ceases Homework...

Homework Statement http://serv1.gulfup.cc/i/00003/ev7u8r04c18k.jpg Homework Equations K1+U1=K2+U2 The Attempt at a Solution I have the solution i am just confused about one point, in the solution, it considred both the translational and rotational kinetic energy for the cylinder on the...

In my electromagnetic theory book, there is a classification of vector fields, one of the 4 different type vector fields is "solenoidal and irrotational vector field" (both divergence-free and curl-free). If solenoidal and rotational vector fields are same thing, then it means the vector field...

i have often come across the sentence "by taking moments" in rotational mechanics, but i really don't understand ,what it is.please explain it(iam not referring to moment of inertia).

When rotation exists, so does the radial acceleration. It can be defined as ar=-ω2xr So there is a kind of acceleration with rotation all the time. Thus, we have to use non-inertial reference frame all the time. Could a rotational movement be analysed in an inertial ref. frame?

about what axis is equation of angular momentum calculated(angular momentum = moment of inertia*angular velocity)? please help.

in Newton's laws of rotational motion, is the net torque calculated only about centre of mass?or is it valid for torque about any axis?

in parallel axes theorem in rotational mechanics,is it necessary that the axes must intersect the body?

Homework Statement I am doing the old frozen can vs liquid can experiment and one of the questions asks that if cans with different diameters were used with the same contents (so same mass relative to diameter size) how would this effect the time taken for the cans to go down a ramp (how would...

So I am given a rotational microwave spectrum of a molecule (CO specifically) and I have to find the constant B if it's not elastic , the constants B and Dj if it is elastic. Anyone know how to do that? :frown:

Homework Statement A 1.5 hp motor drives a machine disk having a mass of 4.5 kg and a diameter of .4 m from rest to a speed of 750 rpm. How long does it take to reach the operating speed? Homework Equations angular momentum torque The Attempt at a Solution I'm not really sure where to start...

Homework Statement A uniform, solid sphere of mass 350 grams and radius 25.0 cm has an axle attached to it tangent to its surface. The axle is oriented horizontally, causing the sphere to be suspended below it, its center of mass directly below the axle. Someone lifts the sphere until its...

Homework Statement In studying for an upcoming exam, one of the concepts introduced was that an object moving translationally will move faster than one moving rotationally. To me that doesn't make sense. So, I do not have a specific problem but really just looking for someone to be able to...

I feel like this is a very simple concept that I seem to confuse more often than I'd like to admit. Namely, if you have a rotating simple pendulum (or really any object), why does it have 0 translational kinetic energy if it is kept rotating around a fixed axis? The centre of mass is constantly...

1. A car door is left open at an angle theta with the side of the car. The door is uniform of mass M and length L. The car accelerates with linear acceleration a. How long does it take the door to close. 2. theta = .5(angular acceleration)t^2 angular acceleration = tangential...

1. A ball of mass m is placed in a smooth groove at the centre of disc and the frame starts to rotate with angular speed w, which if the following statement are incorrect? 1) Net force on the ball is towards center. 2) Motion of ball is in radially outward direction w.r.t center. 3)...

I don't really understand the difference between uniform circular motion and rotational motion. I know that uniform circular motion deals with a body that is orbiting around a central point, with a centripetal force that is causing it to move in a circle. I know that rotational motion uses...

Why is rotational equilibrium condition independent of origin about which torques are taken?

Homework Statement I attached the stated questions. Mainly need help with question 2. See below for my answer to question 1.Homework Equations ΣT=Iα ΣF=ma moment of inertia of sphere: I=(2mR^2)/5 moment of inertia of disk: I=(mr^2)/2 v=rω V(center of mas)=V(tangential) -because of smooth...

I'm trying to determine how powerful of a stepper motor I need for a project. I am attempting to take a display that weighs 15lbs and transition it from laying flat to inclined (approximately 45 degrees) using a stepper motor. I had considered a linear actuator since it would have been an easier...

Homework Statement A cylinder of known mass M, radius R, and rotational inertia I is placed on an inclined plane with angle θ. A string is wound around the cylinder and pulled up with a tension T parallel to the inclined plane. The coefficient of static friction is large enough to prevent...

I have a question regarding the rotational energy equation, derived based on the rigid rotor assumption: ##\epsilon = k\theta_r J (J+1)## where k = Boltzmann constant, and J is the rotational quantum number. The degeneracy is 2J+1. Let's assume the constant quantity ##k\theta_r## = 1 and...

Homework Statement A baseball is thrown at 85 mph and is thrown with a spin rate of 125 rpm. The distance between the pitchers point of release and the catcher’s glove is 60.5 feet. How many full turns does the ball make between release and catch? Homework Equations Vf^2=V0^2+2a(Δ x) X=...

I was curious about what forces can be applied to a molecule to cause a rotational emission.

Here is the problem I am working on. I have found answers for all of them except part (f), which is the one I need help with. I will report the answers I have so far: A classic 1957 Chevrolet Corvette of mass 1240 kg starts from rest and speeds up with a constant tangential acceleration of 2.00...

Homework Statement A computer disk drive is turned on starting from rest and has constant angular acceleration. If it took 0.680s for the drive to make its second complete revolution, how long did it take to make the first complete revolution? (t=?) Homework Equations Θ=(ct^2)/2 (i think) The...