Rotational Definition and 1000 Threads

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...

Homework Statement a) A 1.5 kg frog sits at rest on top of a solid disk. The disk's mass is 4 kg, its radius is 1.25 m, and it rotates on a frictionless axle. The frog jumps from the disk at 3.7 m/s at an angle of 50°. Find the angular momentum of the frog about the axle as it leaves the disk...

Homework Statement A hard drive consists of a rigid circular platter (or disk) of radius 0.05 m and thickness 0.002 m. In normal operating conditions, the hard drive spins at 7200 rotations per minute. The read/write head is a light metallic element that floats just above the platter and both...

My book on Physics by Beiser specifies that the rotational energy levels of a diatomic molecule are given by J(J+1)/ℏ2, where J = 0, 1, 2, 3, ... . However, in the next page, it goes on to mention that the lowest rotational energy level corresponds to J = 1. I don't see why that shouldn't...

Homework Statement A cyclinder of mass m and radius r is rotated about its axis by an angular velocity ω and then lowered gently on an inclined plane as shown in figure. Then: (a) It will start going upward. (b) It will first go up and then downward. (c) It will go downward just after it is...

Homework Statement I'm given the following diagram And asked to find the transfer function G(s) = \frac{X(s)}{T(s)} and seem to be having some difficulty doing so. Homework Equations The Attempt at a Solution Apparently this is free body diagram I seem to be having difficulty...

I found an interesting paper... Dark Energy and Dark Matter as Inertial Effects A globally rotating model of the universe is postulated. It is shown that dark energy and dark matter are cosmic inertial effects resulting from such a cosmic rotation, corresponding to centrifugal and a...

The velocity of any point P of a rigid body in rotation plus translation is \vec{}vp=\vec{}vCOM+\vec{}vp,COM. Now |\vec{}vCOM|=v and \vec{}vp,COM =rω . But v and rω are same thing as v=rω ,so velocity of the particle every time will be √2 v.Then what is the difference between \vec{}vCOM and...

http://www.aapt.org/physicsteam/2010/upload/2009_F-maSolutions.pdf Homework Statement Two discs are mounted on thin, lightweight rods oriented through their centers and normal to the discs.These axles are constrained to be vertical at all times, and the discs can pivot frictionlessly on...

Mass 1 is located at the far left end of a 90 cm beam. Mass 2 is located at the center of the beam, and mass 3 is located 30 cm from the center, on the right side. Mass 3 and mass 1 are the same. If the fulcrum is located 10 cm to the left of the center of the beam, what is the mass of mass 2 if...

Hello, I have a problem that I have not been able to solve Homework Statement Here is the problem question: A bowling ball rolling at 8 m/s begins to move up an inclined plane. What height does it reach? Homework Equations The equation that I used was the formula relating...

Hellow! I was noting that several definitions are, in actually, expressions of vector calculus, for example: Jacobian: \frac{d\vec{f}}{d\vec{r}}=\begin{bmatrix} \frac{df_1}{dx} & \frac{df_1}{dy} \\ \frac{df_2}{dx} & \frac{df_2}{dy} \\ \end{bmatrix} Hessian: \frac{d^2f}{d\vec{r}^2} =...

Homework Statement A solid wood door 1.00 m wide and 2.00 m high is hinged along one side and has a total mass of 49.0 kg. Initially open and at rest, the door is struck at its center by a handful of sticky mud of mass 0.500 kg, traveling perpendicular to the door at 15.0 m/s just before...

Hi All, Assume we have a package that we want it in an orbit with highest possible speed. In which orbit (low,mid,high) the package will rotate faster ? Due to smaller distance, low Earth orbit should allow more speed but there is also more air friction there. What would be the mathematical...

Hey, I've been struggling a little with rotational mechanics in my AP physics, any ideas for good resources to help? Thanks a lot in advance.

How does one go about making a damper for a rotating system? Let's say we have a wind-up toy, and we want it to go slower, or something like that. Sorry for such a basic question, but I can't really figure out a decent way to do this. Any ideas?

Homework Statement Answer: C Note: Sorry admins for the picture, needed to include the diagram though. Homework Equations ∑\tau = I\alpha ∑F = ma a = \alphar The Attempt at a Solution The torques must be balanced (is this reasoning already wrong?), thus, F*R1 = F_T*R2 F_T =...

Homework Statement A 0.70-kg disk with a rotational inertia given by MR^2/2 is free to rotate on a fixed horizontal axis suspended from the ceiling. A string is wrapped around the disk and a 2.0-kg mass hangs from the free end. If the string does not slip, then as the mass falls and the...

Homework Statement A 8.0-cm radius disk with a rotational inertia of 0.12 kg*m^2 is free to rotate on a horizontal axis. A string is fastened to the surface of the disk and a 10-kg mass hangs from the other end. The mass is raised by a using a crank to apply a 9.0-N*m torque to the disk. The...

can we convert the linear motion into rotational motion in cars using a fly wheel under the car ?

Ok so I roughly know what rotational motion is (e.g. the spinning of a DVD) but I wish to know the textbook definition for it. I tried Googling it but to no avail. The first link on Google gives this: http://en.wikipedia.org/wiki/Rotation_around_a_fixed_axis But as mentioned above, that...

I'd like some help justifying the approximation that the vibrational and rotational motion of a diatomic molecule is separable. For two atoms of masses m1 and m2 the full hamiltonian is H=-\hbar ^2 /2m_1 \nabla _1 ^2 - \hbar^2 /2m_2 \nabla _2 ^2 + V(r-r_0) Where V(r-r0) is the potential...

Homework Statement Consider a uniform rod of mass 12 kg and length 1.0 m. At its end, the rod is attached to a fixed, fricition free pivot. initially the rod is balanced vertically abbove the pivot and begins to fall (from rest) as shown. Determine a) the angual acceleration of the rod as...

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Hey PF! Homework Statement I've attached the problem to this post along with my free body diagram. Homework Equations Moment of inertia of a cylinder: 1/2MR^2The Attempt at a Solution Since the cylinder is moving at a constant velocity and is not slipping, ƩF = 0. For the torques around the...

Homework Statement This isn't so much of a problem as a general question. I am trying to find the starting velocity of a spinning ball going upwards (in air, close to Earth's surface, only force acting on it is the gravitational force) until its linear velocity reaches zero. I found the initial...

Homework Statement A large wheel has a radius of 7.1 m. A rope is wrapped around the edge of the wheel and a 7.6 kg box hangs from the rope. A smaller disk of radius 1.38 m is attached to the wheel. A rope is wrapped around the edge of the disk as shown. An axis of rotation passes through the...

Good afternoon! I've been mulling over this question for a bit and I can't seem to understand what it is asking. This is a question for an introductory calculus-based physics university course. 1. The Problem: A uniform disk, such as a record turntable, turns 8.0 rev/s around a frictionless...

Homework Statement A light rigid cylinder of radius 2a is able to rotate freely about its axis, which is horizontal. A particle of mass m is fixed to the cylinder at a distance a from the axis and is initially at rest at its lowest point. A light string is wound on the cylinder, and a steady...

Homework Statement A 240g ball and a 570g ball are connected by a 48.0-cm-long massless, rigid rod. The structure rotates about its center of mass at 110 rpm. Homework Equations KE = Iω^2 I = 1/12(mr^2) The Attempt at a Solution Since it has two masses and two different radius...

Homework Statement Hello, I am a bit confused on when rotational kinetic energy exists and when linear kinetic energy exists. For example when we spin a string with a ball attached to the end it has kinetic energy of 0.5mv^2 of the ball when we were solving for velocity of the ball at certain...

Sorry, this isn't a question from a book or something, but I wasn't sure where else to put this. Is there a convenient way of memorizing or deriving the following?: I have an exam in a week and I thought I might as well try asking before making flashcards.

I think I on the rigth track, would you revise it please 1. A motor is connected to a solid cylindrical drum with a radius of 0.6m and a mass of 52kg. A massless rope is attached to the drum and tied at the other end to a 38kg weight so the rope will wind onto the drum as it turns. The weigth...