What is Rotational: Definition and 1000 Discussions

A rotation is a circular movement of an object around a center (or point) of rotation. The geometric plane along which the rotation occurs is called the rotation plane, and the imaginary line extending from the center and perpendicular to the rotation plane is called the rotation axis ( AK-seez). A three-dimensional object can always be rotated about an infinite number of rotation axes.
If the rotation axis passes internally through the body's own center of mass, then the body is said to be autorotating or spinning, and the surface intersection of the axis can be called a pole. A rotation around a completely external axis, e.g. the planet Earth around the Sun, is called revolving or orbiting, typically when it is produced by gravity, and the ends of the rotation axis can be called the orbital poles.

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  1. C

    Why is rigid body rotational energy not exactly applicable to fluids?

    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...
  2. soothsayer

    Bernoulli Equation for Rotational Flow

    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...
  3. I

    Calculating the Rotational Inertia

    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...
  4. C

    Rotational Dynamics in a Pully

    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...
  5. H

    What's wrong with this derivation for rotational energy of a sphere?

    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...
  6. B

    How do I calculate the maximum rotational speed of a hollow cylinder?

    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...
  7. L

    Mastering Physics: Rotational Motion Around Two Cylinders

    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...
  8. jaumzaum

    Rotational dynamics - direction of friction

    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...
  9. L

    Rotational Motion Around Two Cylinders

    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...
  10. B

    The rotational analog of Ehrenfest's Theorem

    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...
  11. jaumzaum

    What happens to rotational inertia when external forces disappear?

    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...
  12. C

    Rotational Equilibrium and Normal Forces

    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...
  13. D

    Friction force in rotational motion

    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...
  14. M

    Two Rotational Dynamics Problem

    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...
  15. A

    Solving Two Physics Questions: Rotational Inertia & Equilibrium Temp.

    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...
  16. Saitama

    Rotational dynamics, semicircular arc

    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!
  17. G

    Solve Rotational Dynamics Homework: Hollow Cylinder, Weight, String

    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...
  18. D

    How do we use this to solve for the spacing between levels?

    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...
  19. D

    Spacing/population of rotational states

    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...
  20. H

    Rotational and Translational Equilibrium Help Needed

    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...
  21. V

    Gravity & Rotational Forces: Is It Possible?

    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...
  22. E

    Question in rotational motion

    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...
  23. E

    Rotational Motion: The Relationship Between Linear and Angular Displacement

    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?
  24. E

    Question in rotational motion

    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...
  25. S

    Simple and quick question on rotational motions

    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...
  26. J

    Finding Rotational Kinetic Energy of Sphere on Ramp

    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...
  27. T

    Rotational Dynamics Problem - Rod slipping against Block

    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...
  28. K

    Conservation of linear momentum and rotational motion

    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...
  29. B

    Increase Of Rotational Inertia While Motion Occurs

    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 =...
  30. B

    Rotational Inertia: Exploring Intuitive Explanations

    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?
  31. B

    Why is torque perpendicular to the plane of rotation in rotational motion?

    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...
  32. A

    Stuck on a rotational kinematics question

    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...
  33. C

    Normal force in rotational motion

    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...
  34. D

    Rotational Dynamics Confusion

    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...
  35. T

    Rotational Mechanics Problem typical one

    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...
  36. T

    Rotational Mechanics Problem again

    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) +...
  37. T

    Rotational Mechanics Problem: Solving for Height Using Energy Conservation

    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...
  38. T

    Finding the Axis of Rotation in a Rotational Dynamics Problem

    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 ...
  39. B

    Rotational Kinetic Energy of Big Ben

    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...
  40. G

    Proving Rotational K.E. Formula?

    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)
  41. G

    How does the type of drill affect the rotational kinetic energy of a gyro?

    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...
  42. S

    Rotational Dynamics - Energy, Torque

    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...
  43. L

    Force on rigid body: translation or rotational acceleration?

    Homework Statement A perpendicular force F acts on the tip of a thin rod of length L and mass M in the ij-plane which is not fixed. What is the translational and rotational acceleration of the rod about the center of the rod? Homework Equations At first it seems like an easy problem...
  44. M

    Rotational Kinematics (String attached to disk)

    Homework Statement Determine the relationship between the angular acceleration of the flywheel, the downward acceleration of the block, and the radius of the ring. Known data: Mass Ring: 1.420 kg Radius Ring (Inside, then Outside): 5.10 cm, 6.325 cm Mass Disk: 1.455 kg Radius Disk...
  45. M

    Find final rotational kinetic energy without knowing radius?

    Homework Statement A 0.125kg basketball is rolling w/out slipping on a horizontal table at 4.50 m/s when it rolls off the edge and it falls to the floor, 1.10 m below. What is the rotational kinetic energy of the ball right before hitting floor?Homework Equations KE rot: .5 I w^2 KE...
  46. S

    Exploring Frictional Forces & Rotational Equilibrium

    Homework Statement When I drag my feet on the ground (on a frictionless surface), there will be an equal but opposite force acting on another body. What is that body exactly?Homework Equations none The Attempt at a Solution Will it be transferred to some other parts to my body? So in space...
  47. S

    Rotational Motion: Energy Conservation

    Homework Statement the sliding block has a mass of .850kg the counterweight has a mass of .420kg , and the pulley has a mass of .350kg with outer and inner radius .030m, .020m, the coefficient of friction is .250. the pulley turns the axle. the light cord does not stretch and does not slip on...
  48. binbagsss

    Rotational and Translational Kinetic Energy - marble and bowl problem.

    A uniform marble rolls down a symmetric bowl, starting from rest at the top of the left side. The top of each side is a distance above the bottom of the bowl. The left half of the bowl is rough enough to cause the marble to roll without slipping, but the right half has no friction because it...
  49. G

    Using Newtons 2nd law for rotational motion

    I've attached an image explaining the problem. All pulleys are massless. Basically, they want me to show some relations between wire tensions, using Newtons 2nd law for rotational motion. This law is written in my book as: dL / dt = torque, where L is angular momentum. I'm not sure...
  50. B

    Kinetic Energy rotational and translational conceptual question.

    Homework Statement A ball rolls without slipping down incline A, starting from rest. At the same time, a box starts from rest and slides down incline B, which is identical to incline A except that it is frictionless. Which arrives at the bottom first? (a) The ball arrives first. (b) The...
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