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. X

    Rotational inertia of a rod that has mass on one end

    Homework Statement a 3 kg mass is on the end of a metal rod which is pivoted at one end. the mass of the rod is 2kg its length is 4 meters Homework Equations I=(ML^2)/3 The Attempt at a Solution the rotational inertia of the rod itself is 10.6 but i don't know how the 3kg mass at the end...
  2. P

    Earth's Rotational Velocity: Find Linear Velocity

    Homework Statement Find the linear (or tangential) velocity of a point on the Earth's equator in the frame of reference about a stationary rotational axis as it spins over the course of one day. Homework EquationsThe Attempt at a Solution I do not understand what the frame of reference is?? If...
  3. P

    Rotational motion - finding tangential acceleration

    1. The problem A 6 kg block is released from a height of 5 m on a frictionless track and goes into a half pipe with a radius of 2 m. Determine the tangential and radial components of the acceleration when the block reaches a height of 2 m.Homework Equations Ac= v^2/r. At = r*angular...
  4. 29ayushmitt

    Rotational Dynamics And Collision

    Can't Even Start Please Help And Soon Exam Tommorow.
  5. F

    Question on Rotational Dynamics of Yoyo

    Homework Statement Please see attached picture. Homework Equations Shown in picture The Attempt at a Solution It's a textbook example that has a solution. At the middle right hand side of the picture, they say "From Eq... Vcm = Rw" (Where 'cm' is centre of mass) I don't understand why this is...
  6. L

    Relating SHM and Rotational Motion

    Homework Statement A spring of stiffness k is attached to a wall and to the axle of a wheel of mass m, radius R, and moment of inertia I = βmR^2 about its frictionless axle. The spring is stretched a distance A and the wheel is released from rest. Assume the wheel rolls without slipping. At...
  7. Q

    Rotational EOM's with non diagonal inertia tensor

    I'm having difficulties understanding how I should calculate the angular velocities of a rigid body when the inertia tensor is given in body coordinates and has off diagonal elements. Let's assume I have an inertia tensor ## I = \begin{bmatrix} I_{xx} & -I_{xy} & -I_{xz} \\ -I_{yx} &...
  8. J

    How Do You Calculate Angular Acceleration from RPM?

    A 61 cm diameter wheel accelerated uniformly about its center from 120 rpm to 280 rpm in 4.0 seconds. Determine the Angular acceleration So I converted the 120 and 280 rev per min to radians per s with 45238.93 rad/s and 105557.51 rad/s and used them as angular velocity final and initial. then...
  9. K

    How can I measure rotational speed of a golf ball and projectiles?

    I'm planning on carrying out an investigation with a golf ball and projectiles. Is there any type of equipment/sensor that I can used to measure the rotational speed/angular velocity? I know a gun chronograph can be used to detect the velocity but what can I used to detect the angular velocity...
  10. H

    Using moon's rotational energy on earth

    Homework Statement Suppose that some time in the future we decide to tap the moon's rotational energy for use on earth. In additional to the astronomical data in Appendix F in the textbook, you may need to know that the moon spins on its axis once every 27.3 days. Assume that the moon is...
  11. G

    Rotational Period of Large Body

    Homework Statement The Sun rotates on its axis every 25 days. The sun currently has a radius of 7X10^8 m. When it expands into a Red Giant (in about 4 billion years) it will have a radius of 1.5X10^11 m. What will its rotational period be assuming the same mass for both, and they are both...
  12. K

    I with rotational kinetic energy problems

    I tried to use this formula: KE=(1/2)(I)(w)^2, and work=change in KEFor the first question, i tried to plug the number into the rotation kinetic energy formula: 3600rpm=376.8rad/s (0.5)(2,000kg)(0.125m)^2(376.8rad/s)^2 I found out this was the answer 1.1 x 106 J, but I got 2218410J For the...
  13. J

    Combining linear and rotational equations of motion

    I have a moving body with constant linear and rotational acceleration. Given a starting condition (position, orientation, linear and angular velocities), how can I combine the equations of motion to give a position and orientation a given time on?
  14. Valerie Prowse

    Rotational energy & rotating rod

    Homework Statement Consider a uniform rod of mass 12 kg and length l.0 m. At its end, the rod is attached to a fixed, friction-free pivot. Initially the rod is balanced vertically above the pivot and begins to fall (from rest) as shown in the diagram. Determine, a. the angular acceleration of...
  15. T

    Equations of motion for a rotational system

    Homework Statement http://postimg.org/image/9fw7awqov/ The question is to write the Laplace transformed equations of motion for the system Homework EquationsThe Attempt at a Solution I am confused about a couple of things: why is an angle is not defined for the rotation of J2. Does it means J2...
  16. S

    Solve Rotational Collision Homework: 100 RPM to 50 RPM

    Homework Statement A 2kg , 0.2 m diameter turntable rotates at 100 rpm on frictionless bearings. Two 0.5 kg block fall from above, hit the turntable simultaneously at opposite ends of the diameter, and stick. What is the turntable's angular velocity (in rpm) just after? Homework Equations L= I...
  17. Z

    Rotational energy on an incline

    Homework Statement A cart whose body has mass M = 1.5 kg is set on four tires each of which has mass m = 0.3 kg and radius r = 0.1 meters. Each tire can be treated as a solid disk with rotational inertia mr2/2. The cart is set on an incline a height h = 1.2 meters high and released. At the...
  18. Y

    Moment of inertia and rotational motion

    Hello, I am currently attempting to cover rotational motion using Halliday's Fundamentals of Physics. I understand very well the concept of moment of inertia as defined as the sum Σmi*ri2. However, the textbook argues that if there are too many particles, the moment of inertia can be defined as...
  19. I

    Equation of motion for a rotational mass and spring system

    Homework Statement A small ball with mass M attached to a uniform rod of mass m and length l pivoted at point o and attached to two springs with spring constant k1 and k2 at distance d1 and d2 from point o as shown in Fig 2. The system oscillates around the horizontal line. Assume the system...
  20. B

    Rotational temperature problem

    Homework Statement Hi there, I have a question that I'm not sure how to go about solving: I've been given a series of transitions in the microwave spectrum of 31P14N and have assigned these Jinitial and Jfinal quantum numbers, calculated the bond length etc. The next part says that when 31P14N...
  21. CaptCoonoor

    Rotational Motion - Disk-Disk Collision problem

    Hey Guys, Can you tell me how to solve this one, Need not give me direct answers but just take a look at this : Consider two disks A and B of equal radius, let m1 be the mass of disk A and m2 be the mass of disk B, Both are moving towards each other with Velocity v1 and v2 respectively, If they...
  22. AdityaDev

    Explaining Rotational Mechanics: Friction and Stationary Disc

    When you put o disc on top of a plank and if you pull the plank, the disc rotates but stays stationary. Here the friction between the plank and disk produces an unbalanced torque and hence it spins.But this friction should also cause an acceleration in the disc right? Then why does it remain...
  23. G

    Finding gravitron rotational frequency

    Homework Statement In an old-fashioned amusement park ride, passengers stand inside a 3.0-m-tall, 5.0-m-diameter hollow steel cylinder with their backs against the wall. The cylinder begins to rotate about a vertical axis. Then the floor on which the passengers are standing suddenly drops away...
  24. M

    Rotational Spring Arbitrary Motion

    What I want to do is model the rotational behaviour of two bodies (1 and 2). They are connected by three virtual rotational springs (representing a link between them). For a normal (translational) spring the forces on body 1 in X, Y, and Z would be easily calculated as: $$ \mathbf{F}_1 =...
  25. Ravenalia

    From rotational KE to translational displacement

    Homework Statement A frictionless pulley has the shape of a uniform solid disk of mass 5.00 kg and radius 28.0 cm . A 1.40 kg stone is attached to a very light wire that is wrapped around the rim of the pulley, and the stone is released from rest. As it falls down, the wire unwinds without...
  26. S

    Rotational Motion - Conceptual

    Homework Statement The lightweight pivoted bar in the figure will be in rotational equilibrium when a 200N force acts (a) down at D (b) up at B (c) down at E or up at C (d) up at C only (e) none of these Homework Equations Torque = Force x Distance ∑Torque= 0 for rotational equilibriumThe...
  27. S

    Connections between Linear and Rotational Quantities

    Homework Statement A wheel of radius R starts from rest and accelerates with a constant angular acceleration α about a fixed axis. At what time t will the centripetal and tangential acceleration of a point on the rim have the same magnitude? Homework Equations acp=r x ω2 at= r x α ω= 2π / T...
  28. F

    Determining the tension on a rotating particle

    Homework Statement [/B] A particle of mass m slides (both sideways and radially) on a smooth frictionless horizontal table. It is attached to a cord that is being pulled downwards at a prescribed constant speed v by a force T (T may be varying) Use F=ma in polar coordinates to derive an...
  29. N

    Calculating CO2 Rotational Constant | J=0,1,2,3,4,5 Excited State Analysis

    Hey! I have a problem. The problem is simple: calculate CO2 rotational constant. I have values for J (ground state and excited state), with those grades I have to calculate rotational constant. I know that for J=0,2,4.. it is just in ground state and for J=1,3,5..it is excited state. But how do...
  30. O

    Rotational kinetic energy(flywheel) problem

    Homework Statement You have been assigned the task of designing a flywheel capable of storing the translational kinetic energy of a 600 kg car traveling at 100 km/hr. The flywheel is to be manufactured out of steel and the maximum rotational speed is 12,000 rpm. a. Assuming that the flywheel is...
  31. S

    Turbine: Straight or Rotational airflow?

    I'm working on a project now and I'd like to know which type of airflow would power a turbine faster/better straight or rotational? Or will rotational airflow even have any effect on the turbine...? P.S. When I say rotational airflow, I mean circular airflow that rotates in the same direction...
  32. B

    How Does Rotational Inertia Affect the Motion of a Sphere on a Moving Ramp?

    1. Homework Statement A solid sphere (mass of m, radius of r and I=2/5 mr2) is rolling without slipping on a rough surface with a speed of v. A ramp (mass of 2m and angle of θ) rests on a smooth surface and is free to slide on the surface. As the ball rolls up the ramp, the ramp begins to move...
  33. H

    A wheel with rotational inertia I = 1/2MR^2

    Homework Statement [/B] A wheel with rotational inertia I = 1/2MR^2 about its horizontal central axle is set spinning with initial angular speed W0. It is then lowered, and at the instant its edge touches the ground the speed of the axle (and CM) is zero. Initially the wheel slips when it...
  34. L

    A rotational tire and tape problem.

    Homework Statement A tire is rolling along a road, without slipping, with a velocity v. A piece of tape is attached to the tire. When the tape is opposite the road (at the top of the tire), it's velocity with respect to the road is Homework Equations v=ω×rThe Attempt at a Solution Well the...
  35. B

    Torque seesaw problem- rotational equilibrium

    Homework Statement A seesaw with a mass of 5 kg has one block of mass 10 kg two meters to the left of the fulcrum and another block 0.5 m to the right of the fulcrum. If the seesaw is in equilibrium, A. find the mass of the second block. B. find the force exerted by the fulcrum I have trouble...
  36. J

    Introductory Rotational Motion Question

    I'm beginning the chapter of Rotational Motion and Angular Momentum and it says the following which got me confused: Source: http://cnx.org/contents/031da8d3-b525-429c-80cf-6c8ed997733a@8.32:68/College_Physics When I was introduced acceleration at the beginning, it was stated that an...
  37. K

    Rotational motion -- Energy stored in a flywheel

    Homework Statement Cylindrical shape pulley ( m = 6 kg, R = 0.18 m) is rotating at a frequency f = 10 s-1. Due to constant torque it stops. Calculate the work done by the breaking force. Homework Equations w = 2πf The Attempt at a Solution [/B] I can calculate the angular velocity: w = 2πf =...
  38. K

    How does rotational motion contribute to an object's total kinetic energy?

    Homework Statement Same mass sphere and cylinder are rolling on a horizontal plane. Which part of each objects kinetic energy does objects rotational energy make up? Homework Equations Erotational = 1/2 Iw2 Ekinetic = 1/2 mv2 The Attempt at a Solution [/B] I know, that moments of inertia...
  39. G

    Equate Kinetic Friction to Rotational Energy?

    Homework Statement So a car owner wants to change his current tires and rims to a wider set of tires and rims for increased handling ability. However, the owner does not want to lose any acceleration performance due to the increased friction of having wider tires. To combat this, the owner...
  40. L

    How Do Two Connected Discs with Masses Affect Angular Acceleration?

    Homework Statement Two discs of radius R and r are fixed to each other, i.e., they rotate together. Strings are wound around both discs and two equal masses M are connected to the ends of the strings (see Figure 1). Find the angular accelerations of the discs, the accelerations of the masses...
  41. S

    Rotational kinematics (mass wrapped around inner hub)

    Homework Statement A bicycle wheel is mounted as in the lab and as shown to the right. This wheel has a mass of 6.55 kg, a radius of R = 38.0 cm and is in the shape of a ring. A mass M = 1.85 kg is attached to the end of a string which is wrapped around an inner hub which has a radius r = 5.40...
  42. Z

    Translational and Rotational energy in rigid bodies

    Suppose I have some sort of rigid body, a solid sphere let's say. For simplicity's sake let's assume that the sphere can only rotate about a single arbitrary axis through the center of mass. If the center of mass of the sphere is traveling with a constant velocity (with respect to some arbitrary...
  43. Q

    Rotational mechanics .hinge reactions

    Rotational Mechanics... Hinges and Normal Reactions -- Please help Could anyone please explain me the reason for two normal reactions on a hinge attached to a door. Also if there are two hinges the direction of the horizontal component of normal reaction is opposite to the direction of the...
  44. F

    Finding Rotational matrix from axis-angle representation

    Homework Statement Given an axis vector u=（-1, -1, -1) , find the rotational matrix R corresponding to an angle of pi/6 using the right hand rule. Then find R(x), where x = (1,0,-1) Homework Equations I found the relevant equation on wikipedia (see attachment) The Attempt at a Solution I feel...
  45. E

    Finding Rotational Speed once the Moment of Inertia Increase

    Homework Statement A trapeze artist performs an aerial maneuver. While in a tucked position, as shown in Figure A, she rotates about her center of mass at a rate of 6.03 rad/s. Her moment of inertia about this axis is 16.1 kg·m2. A short time later the aerialist is in the straight position, as...
  46. P

    Algebra of pulley-mass energy equation

    Homework Statement [/B] A 0.20-kg block and a 0.25-kg block are connected to each other by a string draped over a pulley that is a solid disc of inertia 0.50 kg and radius 0.10 m. When released, the 0.25-kg block is 0.30 m off the ground. What speed does this block have when it hits the ground...
  47. N

    How Does Child Movement Affect Torque and Force Distribution on a Plank?

    Homework Statement A child of mass m is supported on a light plank by his parents, who exert the forces F1 and F2 as indicated. Find the forces required to keep the plank in static equilibrium. Use the right end of the planks as the axis of rotation. ( Answer: F1=(1/4)mg, F2=(3/4)mg )...
  48. T

    Rigid Body Rotational or Translational ?

    In the figure A has mass 4 kg. B and C are identical uniform discs, each of mass 2 kg. The string supporting A is ideal. Obtain the acceleration of A I have just one question, Why is pulley C undergoing translational motion ?, it should be rotational motion because it rotates about a fixed axis
  49. maxhersch

    Work and Rotational Kinetic Energy (Falling Chimney)

    Homework Statement A tall, cylindrical chimney falls over when its base is ruptured. Treat the chimney as a thin rod of length 49.0 m. Answer the following for the instant it makes an angle of 32.0° with the vertical as it falls. (Hint: Use energy considerations, not a torque.) (a) What is the...
  50. O

    Rotational motion- potential and kinetic energy

    http://i.imgur.com/0RtN9Ui.png?1 I am trying to find the linear velocity of the sphere as it leaves the cliff. 2. Homework Equations : Moment of inertia of a sphere: I= 2/5 mr2 3. My attempt at a solution: I know that I am supposed to solve this through the conservation of energy, but would...
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