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. BenGuise

    How to calculate the rotational friction of square axle

    How would I calculate the frictional torque of rotating an axle with a square cross section? The axles that I’m using to drive a gear box are rectangular instead of cylindrical like normal axles, so I’m trying to figure out how much more a motor has to work to turn a square axle than it does to...
  2. S

    I Frame Dragging Direction for Outward Moving Test Mass

    I have the following question considering frame dragging: A test mass starting at rest near a rotating mass or with an initial velocity pointing towards the center of the rotating mass will be deflected in such a way that it begins to move around the mass in the rotational direction. This is...
  3. P

    Torque acting on a particle in rotational motion

    Homework Statement The following question involves a torque acting on a particle in rotational motion. It provides practice with the various equations for angular velocity, torque etc A particle of mass ##m## initially has position...
  4. starstruck_

    Angular momentum and rotational inertia

    Homework Statement You decide to design a bicycle that will have only 3/4 of the angular momentum of the original wheel when both wheels are traveling along a road at the same velocity. The original wheel had a diameter of d1=37cm and rotational inertia of I1=0.32 m2kg. If your new wheel has a...
  5. ARNAV SHARMA

    Rotational Mechanics: Find Height of Stick in N Turns

    Homework Statement A student throws a stick of length l up in the air .At the moment the stick leaves his hand ,the speed of the stick's end is zero.The stick completes N turns just as it is caught by the student at the initial release point . Show that the height to which the centre of mass...
  6. O

    Lagrangian equations of particle in rotational paraboloid

    Hello. I solve this problem: 1. Homework Statement The particles of mass m moves without friction on the inner wall of the axially symmetric vessel with the equation of the rotational paraboloid: where b>0. a) The particle moves along the circular trajectory at a height of z = z(0)...
  7. S

    Rotational Inertia and Angular Momentum

    Homework Statement A disk with a rotational inertia of 8.38 kg·m2 rotates like a merry-go-round while undergoing a torque given by τ = (5.03 + 1.01t) N · m. At time t = 1.00 s, its angular momentum is 6.57 kg·m2/s. What is its angular momentum at t = 3.00 s? Homework Equations dL/dt= T...
  8. P

    Rotational Symmetry in MCNPX core design

    Designing a PWR core in MCNPX for burnup using 4 folds rotational symmetry to reduce computational time of the core, taking reflective boundary conditions on rotational symmetry planes. should the power be reduced to 1/4th of original power (3000 MWth) in burnup card or does the reflective...
  9. M

    Problem of rotational motion

    Homework Statement An airplane propeller is 2.78 m in length (from tip to tip) and has a mass of 127 kg . When the airplane's engine is first started, it applies a constant torque of 1880 N⋅m to the propeller, which starts from rest. Part D What is the average power output of the engine...
  10. J

    Rotational Equilibrium Question

    Homework Statement A bar of uniform density, length L, and mass m is suspended by two ropes of tensions T1 and T2 at either extremity of the bar. The bar is tilted such that it makes an angle θ with the ropes. A mass M is resting at a distance l from T1. https://i.imgur.com/vLlAJbe.png If...
  11. MARX

    BEISER MODERN PHYSICS Rotational Energy Level

    Homework Statement The rotational spectrum of HCl contains the following wavelengths: 12.03 10 5 m 9.60 10 5 m 8.04 10 5 m 6.89 10 5 m 6.04 10 5 m If the isotopes involved are 1H and 35Cl, find the distance between the hydrogen and chlorine nuclei in an HCl molecule. Homework Equations E...
  12. yrjosmiel

    Other symbols for rotational inertia?

    So I'm currently doing a project on motors. It just so happens that I'm dealing with both electrical current and rotational inertia. I have one small problem. The symbol for electrical current is I. But so is rotational inertia! Are there any other symbols for rotational inertia/electrical...
  13. S

    Rotational Motion in Newtonian Mechanics

    Homework Statement Given an plate that has 2 pins attached to it. Each pin has a single balanced circular disc firmly attached to it. Each pin can rotate on their axis in both clockwise and anti clockwise direction. (See image below) Now, assume the discs are rotating with the same angular...
  14. rkatcosmos

    What is the rotational velocity of hard disk actuator arm?

    0 down vote favorite There is a lot of material discussing the rotational speed of the magnetic disk in HDD but not about the rotational speed of actuator arm. What are the typical actuation speeds of the actuator in HDD? This information will be used in the design of a fast shutter system...
  15. G

    Rotational kinetic energy decreases, internal increases?

    If rotational kinetic energy of a closed system decreases, another form of energy must increase for the conservation of energy of a closed system. We assume this system (a person in rotation) has these forms of energy: ΔE=ΔK (only rotational around an axis) + ΔUi (internal) + ΔEt (thermal) with...
  16. P

    Automotive Calculating Rotational Torque of Prime Mover

    I need some outside opinions on determining the available torque on a prime mover. I have a mechanical advantage prime mover (or driver) that creates rotation of its overall mass via a series of offset mass movements within the driver. It's primary power source is gravity; however, movement is...
  17. P

    Calculate Rotational Torque: 8700 kgm2 @ 18 RPMs

    Hey guys and gals. I need someone to double check my math. I have a wheel with a MOI = 8700 kgm2. It is rotating at 18 RPMs. T=MOI*angular acceleration? Or 8700 kgm2 * 1.83 rad/sec= 15979.6 Nm?
  18. Pushoam

    Rotational velocity of the ring

    Homework Statement Homework EquationsThe Attempt at a Solution Wrt inertial frame with origin at the pivot, [/B] The final angular velocity of the ring, the bug are ## \vec ω_r ## and ## \vec ω_b ## and the final velocity of the bug is ## \vec v_b ##. Since, there is no net external...
  19. G

    Calculating Rotation Period of a Collapsing Interstellar Cloud

    Homework Statement A uniform, spherical cloud of interstellar gas has mass 2.03×1030 kg and radius 1.03x1013m and is rotating with period 1.43×106 years. The cloud collapses to from a star 7.03x108m in radius. Find the star's rotation period. Homework Equations I1ω1=I2ω2 Θ=ωt The Attempt at a...
  20. G

    Rotational Torque/Force Problem (rod around hinge)

    Homework Statement A Rod of Mass "M" is attached to a two-way hinge on the floor. It is being pulled by a spring (extension spring, so force is pulling the rod to the right, causing it to move clockwise). The hinge is frictionless. the rod has a mass of 5kg evenly distributed the pulling...
  21. G

    Angular velocity tank receiving cereal

    Homework Statement The cylindrical container, when empty, has the moment of inertia of 2.0 Kgm^2 around the axis of rotation. It is rotating freely on its axis 20 revolutions per minute, when it begins to receive cereal, which falls vertically along its axis at the rate of 0.5 kg-1. The radius...
  22. G

    How to Determine Velocities for Rolling Objects on an Inclined Plane?

    Homework Statement Side by side on the top of an incline plan with height=2 meters a cylinder (Ic= MR^2/2) and a sphere (Ie=2MR^2/5) with equal radius, that come down to the base, rolling without slipping. Mass of the cylinder = 2.0 kg; Mass of a sphere=4.0 kg. Homework Equations $$K_r= 1/2...
  23. S

    Rotational Motion Question, lever arm with two masses

    Homework Statement [/B] A uniform rigid rod with mass Mr = 2.7 kg, length L = 3.1 m rotates in the vertical xy plane about a frictionless pivot through its center. Two point-like particles m1 and m2, with masses m1 = 6.7 kg and m2 = 1.6 kg, are attached at the ends of the rod. What is the...
  24. S

    Have a problem with this Rotational Motion question

    Homework Statement [/B] A wheel, of radius 200mm, rolls over the top of a hill with a speed of 20m/s and negligible friction losses. (I = 1/2mr^2) Homework Equations [/B] Find the speed of the wheel when it is 10m below the top. The Attempt at a Solution [/B] mgh = 1/2mv^2 + 1/2IW^2 W=...
  25. Faefnir

    Calculate Intensity of Braking Moment - Rotational Movement Flywheel

    A flywheel with a inertia moment of ##245 kg \cdot m^2## rotates making 20 round per second. The wheel stops 20 minutes after a braking moment action. Calculate the intensity of the braking moment $$ \omega = 20 \frac{round}{s} = 126 \frac{rad}{s} $$ $$ t = 20 min = 1200 s $$ The braking...
  26. baldbrain

    Change in Earth's gravity & rotational KE due to changes in Radius

    Homework Statement Let g be the acceleration due to gravity at the Earth's surface and K be the rotational kinetic energy of the Earth. Suppose the Earth's radius decreases by 2%. Keeping all other quantities constant, (a) g increases by 2% and K increases by 2% (b) g increases by 4% and K...
  27. ILOVEPHYSIC

    How Does the Rotational Inertia Affect Rolling Motion on an Inclined Plane?

    A uniform wheel of mass 14.0 kg is mounted rigidly on a massless axle through its center, as shown in the figure below. The radius of the axle is 0.200 m, and the rotational inertia of the wheel-axle combination about its central axis is 0.600 kg·m2. The wheel is initially at rest at the top of...
  28. K

    Ratio of rotational inertias for belt-connected wheels

    Homework Statement Wheels A and B as shown in the figure are connected by a massless belt that does not slip. The radius of A is R and the radius of B is r. What is the ratio of rotational inertias ##\frac{I_a}{I_b}## if the two wheels had the same angular momentum about their central axes...
  29. T

    Statics and Rotational Dynamics

    Homework Statement A thin walled spherical shell with a mass of 0.605 kg and a radius of 0.0402 is released, from rest, at the top of an incline. The spherical shell rolls down the incline without slipping. The spherical shell takes 7.49 s to get to the bottom of the incline. A solid sphere...
  30. K

    Rotational Inertia formula help

    A 24 kg solid door is 220 cm tall, 95 cm wide. What is the door's moment of inertia for rotation about a vertical axis inside the door, 17 cm from one edge? I've looked at examples of how to do this problem. They connect it to center mass but I get confused when determining what the center mass...
  31. C

    When is the net torque=0?

    Homework Statement A child is initially sitting near the outer rim of a revolving merry-go-round. Suddenly, the child moves towards the center of the merry-go-round (while it is still revolving). For the merry-go-round+child system, let the symbols L and K refer to the magnitude of the angular...
  32. Redwall54

    Torque and rotational equilibrium question

    Homework Statement 8. A 20 kg uniform beam 10m long is attached to a wall with a cable. The cable is attached to the middle of the beam at a 90 degree angle to the beam. A box of mass 5 kg is also suspended from the beam. In addition to this, the beam is attached to the hinge at the bottom...
  33. L

    Relate rotational kinetic energy to potential energy

    Homework Statement This problem is from the 2015 AP Physics C Mechanics free response, question 3 part b. https://secure-media.collegeboard.org/digitalServices/pdf/ap/ap15_frq_physics_c-m.pdf Homework Equations K = 1/2Iω2 U = mgh The Attempt at a Solution The potential energy of the bar when...
  34. H

    Rotating rod returning to its initial position

    Homework Statement A uniform rod (mass 'm', length 'l') held horizontally above the ground. It is released from its supports and struck vertically upwards at one end. With what impulse should the rod be struck if it is to return to exactly its starting position and orientation? Homework...
  35. Janet1234

    Drawing free body diagrams (torque; rotational motion)

    Homework Statement A 500-N person stands 2.5 m from a wall against which a horizontal beam is attached. The beam is 6 m long and weighs 200N (see diagram below). A cable attached to the free end of the beam makes an angle of 45 degrees to the horizontal and is attached to the wall. Homework...
  36. S

    I Effect of rotational inertia on gravity or visa versa

    Hi, I wonder if a gravitationally bound system ...like a binary star system (or a spinning galaxy for that matter) has a similar inertia in its rotational axis like your classic spinning top? Is there resistance to a change in the axis? I appreciate the system is not solid and so not obviously...
  37. floraha

    Rotational motion down an incline (ring/hoop)

    Homework Statement A 24kg metal ring with 24cm diameter rolls without slipping down a 30 degree incline from a height of 3.4 m. 1) According to the law of conservation of energy what should be the linear speed of the ring at the bottom of the ramp 2) if the ring has a moment of inertia of...
  38. A

    Rotational Inertia of Solid Sphere Suspended from Ceiling

    Homework Statement A solid uniform sphere of radius R and mass M has a rotational inertia about a diameter that is given by (2/5)MR^2. A light string of length 3R is attached to the surface and used to suspend the sphere from the ceiling. What is its rotational inertia about the point of...
  39. A

    What Causes Discrepancies in Calculating Initial Angular Velocity?

    Homework Statement A wheel rotates with a constant angular acceleration of π rad/s^2. During a certain time interval its angular displacement is π rad. At the end of the interval its angular velocity is 2π rad/s. What is its angular velocity at the beginning of the time interval? Homework...
  40. R

    Difference between vibrational, rotational and electron temperature

    I am trying to explain the following statement in my own words... Would it be correct to say that.. I am unsure if a vibrational state is simply a different energy state or something more specific? Do the electron temperature, vibrational temperature and rotational temperature all...
  41. B

    [PoM] Average rotational energy

    Homework Statement Determines the average energy of rotation (per molecule) of a rarefied gas of HF at T = 50 K, knowing that the wave number of rotational absorption for the transition L = 2 → 3 worth 121.5 cm-1. [Hint: it performs the calculation by limiting the number of levels taken into...
  42. Arman777

    Maximum Height of Ball on U-Shaped Ramp

    Homework Statement From an İnitial Lenght h,a solid ball rolls smoothly down one side of a U-shaped ramp and then moves up the other side,which is frictionless.What maximum height does the ball reach ? Homework Equations Energy conservation equations The Attempt at a Solution...
  43. Y

    Rotational Mechanics Question.

    Homework Statement A tangential force F acts at the top of a thin spherical shell of mass m and radius R. Find the acceleration of the shell if it rolls without slipping. Homework Equations Since the shell is rolling, friction does not act at the bottom. So equating the torque, F*R= I*α The...
  44. Arman777

    Studying Trying to Understand Rotational Motion

    I am really troubling to understand the rotational motion concept.Like angular accceleration,angular velocity torque ext.I don't know, I listened my professor's video lectures, I looked some online course pdfs but I need to learn the basics and I need more basic practice for simple...
  45. Arman777

    Rotational Motion - Understanding the Idea

    1- I am trying to understand the rotational motion and In most books there's ##\vec θ## unit vector which its, ##\vec θ=(-sinθ,cosθ)## I can see that If ##\vec r## unit vector is,##\vec r=(cosθ,sinθ)## then , ##\frac {d\vec r} {dt}=\vec θ## Like calculating ##\vec v=\frac {d\vec r}...
  46. quantumSpaghetti

    I Rotational excitation of quantum particle

    I was watching a lecture and there was a connection drawn between classical rotational energy and quantum rotational excitation. The energy of a rotating system is $$E = (L^2) / 2 I $$ with L being the angular momentum and I the moment of Inertia. Then to make it quantum$$ n^2 * ħ^2$$ was...
  47. Duke Le

    Where is wrong in this proof for rotational inertia ?

    Homework Statement Prove the formula for inertia of a ring (2D circle) about its central axis. Homework Equations I = MR^2 Where: M: total mass of the ring R: radius of the ring The Attempt at a Solution - So I need to prove the formula above. - First, I divide the ring into 4...
  48. H

    Scaling Rotational Inertia - from Model to Full Size

    Homework Statement If we multiply all the design dimensions of an object by a scaling factor (f), its volume and mass will be multiplied by f^3. a) By what factor will its moment of inertia be multiplied? b) IF a 1/48 scale model has rotational kinetic energy of 2.5 Joules, what will be the...
  49. H

    Falling Mass on a Pulley - Rotational Energy

    Homework Statement A frictionless pulley has the shape of a uniform solid disk of mass 2.50 kg and radius of .2 m. A 1.50 kg mass is attached to a very light wire that is wrapped around the rim of the pulley, and the system is released from rest. a) How far must the stone fall so that the...
  50. H

    Rotational Dynamics Designing a Propeller Velocity/Acceleration

    Homework Statement You are asked to design an airplane propleller to turn at 2400 rpm. The forward airspeed of the plane is to be 75.0 m/s, and the speed of the tips of the propeller blades through the air must not exceed 270 m/s. What is the maximum radius the propeller can have? With this...
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