Rotational Definition and 1000 Threads

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. J

    I The proportion of kinetic energy of a rotating rigid body?

    The kinetic energy of a rotating rigid body is given by K=1/2mv^2 + 1/2Iw^2 but how to determine the proportion of translational energy and rotational energy? I know that if the mass distribution is more concentrated at its center mass, then more energy goes to the translational part. But is...
  2. dcmf

    Compare rotational inertia of 2 paper cups in 2 diff orientations

    Figure 1: I assume this is a conceptual question regarding the usage of the above inertia equations but the axes are really confusing me. I would imagine that around I1 and I3, you could say that the total inertia is just the sum of all the ring-shaped "slices" of the paper cups (i.e. use the...
  3. dcmf

    Avg Power in a Rotational Energy/Work Problem

    This question has multiple parts and according to all the work done up to this point... How much work W does the motor do on the platform during this process? 1885 J What is the rotational kinetic energy of the platform Krot,f at the end of the process described above? 1885 J What is the...
  4. Malwina

    Minimal rotational kinetic energy for a gyroscope to precess

    TL;DR Summary: I cannot find any information on how to calculate min. KErot at which the gyroscope does not fall over I am doing a project for school in which I investigate energy loss in a gyroscope. I apply a torque on a gyroscope to initiate its rotation and then measure the time it takes...
  5. MP97

    B Rotational Kinematics -- questions about a=mg sin(theta) / (m+I/R^2)

    Hi, I am learning. Rotational Kinematics and I was given this formula in class: a=mgsin(theta)/(m+I/R^2); however, I couldn't understand the professor's explanation of where it comes from. Could someone provide some insights about it? I appreciate any help you can provide.
  6. P

    I Spectroscopy: vibronic and rotational transitions

    In spectroscopy, the highest peaks in the absorption spectrum are those that are associated with the most probable energy transitions in a molecule. The most probable transitions are those in which the best superposition between the wave function of the vibronic level of the fundamental state...
  7. S

    Engineering Measuring rotational speed for Tachometer vs Oscilloscope

    Question: Why does the oscilloscope double almost the exact value of rotational speed measured by Tachometer? Rotational speed from Tachometer = 1930 [RPM] Frequency of 1 period = 64.3 [Hz] which means 3857.91 [RPM] The output waveform of hall-effect sensor is attached. Can you have any...
  8. M

    Rotational inertia of square about axis perpendicular to its plane

    For this problem, How do we calculate the moment of inertia of (2) and (3)? For (3) I have tried, ##I_z = \int r^2 \, dm ## ## ds = r ## ##d\theta ## ##\lambda = \frac {dm}{ds}## ##\lambda ## ##ds = dm ## ## \lambda r ## ##d\theta = dm ## ##I_z = \lambda \int r^3 d\theta ## ##I_z = \lambda...
  9. tracker890 Source h

    Why Is Taking Moments at Point A' Incorrect in Rotational Balance Problems?

    Please help me to understand why it is wrong to take moment for point ## A’ ## , because I think static equilibrium should be static equilibrium for any point in space. Method 1： $$ \sum{M_A=0:} $$ $$ F\cdot R=\left( F_p \right) _x\cdot \left( R-y_p \right) +\left( F_p \right) _y\left( x_p...
  10. V

    Satellite mechanics: linear and rotational momentum

    [This is a continuation of OP's thread here: https://www.physicsforums.com/threads/satellite-mechanics-linear-and-rotational-momentum.1046963/ ] satellite mechanics: linear and rotational momentum I'm trying to better understand classical mechanics, and came up with a question: Say we have a...
  11. D

    A dial can spin on a fixed rotational axis

    What I have done is on my Ipad that I cant upload or at least don't know how to... :/ With hope of help DJ
  12. Y

    Calculate the angular momentum of this particle in rotational motion

    i,j,k arevector I know L=P*r=m*v*r=m(acosωti+bsinωtj)*(-aωsinωti+bωcosωtj)=mabw((cos^2)ωt+(sin^2)ωt)k=mabωk. but why m(acosωti+bsinωtj)*(-aωsinωti+bωcosωtj)=mabw((cos^2)ωt+(sin^2)ωt)k.I need some detail. please help me.
  13. V

    I Satellite mechanics: linear and rotational momentum

    satellite mechanics: linear and rotational momentum I'm trying to better understand classical mechanics, and came up with a question: Say we have a squared satellite weighting 100kg, 1 meter on each side. it has a thruster on it's side, shown in picture thruster quickly ejects 100g of propellant...
  14. alichoudhry57

    I Torque and Rotational Kinetic Energy Relationship

    I am wondering if it is possible to calculate either the Kinetic Energy or Rotational Kinetic Energy of an object if we have the Power (kW), Torque (Nm), and Speed (RPM) of the object.
  15. P

    I What is the purpose of the vector α in the rotational work integral?

    This brief worked example from a textbook section on the method of images is confusing me. Specifically I am confused about the vector α in the integral on the last line. When α (or θ) is an angle, I've only ever seen the vector quantity α (or θ) as a polar vector in the plane. But here...
  16. F

    Intuition on the direction of friction in a rotational dynamics problem

    The figure illustrates the situation. The radii of the larger and smaller discs are 2R and R, respectively. Their masses are M and 2M, respectively (the largst disc has the smallest mass). Also, m=5/4 M, where m is the mass of the suspended object. The pulley is "massless" (negligible moment...
  17. Anmol Dubey

    Calculating final rotational speed from angular velocity

    I have no idea how to go about this. Any help would be appreciated thanks :) Edit: I converted the 1.5 rev/s to rad/s = 9.4 rad/s
  18. chwala

    Find order of rotational symmetry for the given shape

    Ok for (1) I would say that the order of rotational symmetry is ##8##. Would that be correct? What about ##4##? For (2) The number of lines of symmetry is ##4##. And if one would say infinity for both (1) and (2) would that be correct?And if you consider a kite. Would the order of...
  19. B

    A Power induced shift in rotational transitions for a diatomic molecule

    Hello! I am analyzing some data from some rotational transitions between 2 electronic energy levels in a diatomic molecule. I noticed that for different runs that covered the same regions, the peaks we observe are shifted with respect to each other when the power of the laser driving the...
  20. I

    I Rotational Orientation of Monatomic Gas: Angular Momentum Effects

    In other words, is there a rotational orientation of each atom in a monatomic gas (and corresponding rotational speed conserving angular momentum) that affects collisions, or does a substance need to have at least 2 atom particles to have the orientation/rotational ability to have particle...
  21. Hari Seldon

    Watt Rotational Speed Regulator's Lagrangian

    I understand that it is a system with two degrees of freedom. And I chose as generalized coordinates the two angles shown in the pic I posted. I am having troubles in finding the kinetic energy of this system, cause the book tells me that the kinetic energy is something different then what I...
  22. A

    I Conversion of Fluid Rotational Force to Rocking Motion

    Does anyone know how to convert the parameters within constraints to equate rocking motion from fluid being mixed through consistent shaking? What I am given: Centrifugal Force Calculations: mass = 0.25 kg angular velocity = 12.57 rad/s radius = 0.045 m What is known about the bag of fluid on...
  23. A

    I Confused about the axis of rotation in rotational motion w/o slipping

    I'm now learning about rotational motion without slipping and it's really hurting my brain to think about. Imagine a cylinder rotating on a flat plane. I can accept that there is both translational and rotational motion. For example, a given point on the circumference of the cylinder follows a...
  24. Afo

    Total KE = Sum of Translational & Rotational KE: Proving the Equation

    Why is the total energy energy equal to the sum of translational kinetic energy and rotational kinetic energy? I understand the derivation KE = 1/2 I w^2 for a rigid object rotating around an axis: sum 0.5 * m_n * (v_T)^2 = sum 0.5 * m_n * (wr_n)^2 = 0.5 * w^2 * sum m_n r_n^2 = 0.5 * I * w^2...
  25. vipers120

    I Modeling a (rotating) mass impact on a preloaded (rotational) spring

    I am trying to model numerically the following system: A rigid body mass is rotating freely around an axis (no rotational stiffness/damping) within a range, let's assume plus-minus 3 degrees for now. Case A. The external forces on the mass are low and keep changing which results in the situation...
  26. Afo

    Confused while reading HRK regarding rotational kinematics

    Pic 1: Pic 2:
  27. R

    I Rolling balls with different rotational inertia

    I am stuck on problem presented about putting golf balls. A stationary golf ball (mass=45g, dia=42mm, solid & homogeneous) is struck by a horizontal force (putter) and ignoring sliding immediately starts rolling on a level putting green. The ball eventually stops due to rolling resistance...
  28. K

    What's the source of increase in rotational energy of carousel?

    A carousel has the shape of a circular disc with radius 1.80 m and a mass of 300 kg. There are two people with masses of 30 and 45 kg out on the edge while carousel rotates with the angular speed 0.6 rad / s. The people move towards the center of the carousel Calculations show that the...
  29. S

    I Static rotational friction: does diameter matter?

    Imagine a bolted joint with a washer between the bolt and the surface. Assuming the washer is always covered by the bolt head so it's getting a consistent load, does the washer's diameter impact the static friction being imparted on the surface? I see two conflicting ways of viewing this...
  30. nazmulhasanshipon

    Finding out the rotational speed of a mass

    **My Attempt:** Here, I considered for 2 kg mass the resultant motion is zero, which means it's acceleration (a) would be zero. So, if we consider the Tension force from the 1.5 kg mass to keep 2 kg mass from falling is L, then 2×9.8-L=ma=2× 0 ⇒ L=19.6 N. But where does the tension force from...
  31. dextercioby

    I Linear & Rotational Motion: Speed of Tip in Lab Frame

    I have a pencil of Iron of length ##L## rotating about its center in a plane at constant angular velocity ##\omega##. The tip of the pencil in Newtonian mechanics has linear velocity ##\frac{\omega L}{2}##. It can exceed ##c##, of course. Now let us complicate this. Assume the center of the...
  32. momoneedsphysicshelp

    Finding Angular Velocity in Rotational Motion Problems

    53 rpm equals 5.55 rad/sec multiply 5.55 by 2pi to get angular velocity of 34.8717 Is the answer 34.8717? What should I have done to more accurately solve the problem with a better understanding? What other steps should I take when solving similar problems? and lastly, Is the mass relevant...
  33. hquang001

    Rotational motion and angular momentum

    mball = 2 kg, mputty = 0.05 kg, L = 0.5 m, v = 3m/s a) Moment of inertia : I = (2mball + mputty ). ¼ L^2 = 0.253125 kg.m^2 Linitial = Lfinal => mputty. v. r = I.ω => ω = (4.mputty.v.r) / I = 0.148 rad/s b) K initial = 1/2 m v^2 = 0.225 J K final = 1/2 Iω^2 = 2.85.10^(-3) J => Kfinal /...
  34. D

    Prove the rotational invariance of the Laplace operator

    Hello, please lend me your wisdom. ##\Delta u=\partial_{x1}^2u+\partial_{x2}^2u+...+\partial_{xn}^2u## ##Rx=\left<r_{11}x_1+...r_{1n}x_n+...+r_{n1}x_1+...+r_{nn}x_n\right>## ##(\Delta u)(Rx)=(\partial_{x1}^2u+\partial_{x2}^2u+...+\partial_{xn}^2u)\left<r_{11}x_1+...r_{1n}x_n...
  35. A

    Confusion about tidal locking and rotational kinetic energy

    Hello! I was reading two things: 1) tidal locking (as explained in the Wikipedia article:https://en.wikipedia.org/wiki/Tidal_locking where it is stated that, because of internal friction caused by the body of water being attracted to the moon and deforming, the kinetic energy of the system...
  36. N

    Which is the best book for studying Rotational mechanics?

    Homework Statement:: Which is the best book that you've read for understanding rotational mechanics ? Relevant Equations:: Kindly let me know. .
  37. warhammer

    Beam resting on 2 pivots | Problem in Rotational Mechanics

    When one of the pivot is pulled, just at that moment a couple is formed due to the normal reaction from the existing pivot and the weight of the bar. From the assumptions given in the question, we can state that the distance between the two forces (N & W) giving rise to the couple is L/2. Using...
  38. Hamiltonian

    A doubt in the rotational analogue of F=ma

    If we have a cylinder rolling on the ground ##\tau = I\alpha## can only be applied about the point in contact with the surface(Instantaneous axis of rotation) and its CoM I don't see why this should be the case. why can the equation ##\tau = I\alpha## only be applied about the axis passing...
  39. D

    Rotational partition function for CO2 molecule

    Hello fellow physicists, I need to calculate the rotational partition function for a CO2 molecule. I'm running into problems because I've found examples were they say this rotational partition function is: ##\zeta^r= \frac T {\sigma \theta_r} = \frac {2IkT} {\sigma \hbar^3}## Where...
  40. J

    Displacement & Angle Theta: Figuring Out Centripetal Force

    For the displacement, how do I figure out the angle theta between the points? And how does the speed at which the string retracts affect the centripetal force?
  41. bieon

    Pendulum, Rotational Inertia and Center of mass

    This is the figure given. My Attempt ##T=2\pi \sqrt\frac {I}{0.5gd}## ##\frac {m_r} {l} ## ##dm= \frac {m} {l}dx## ##dI = dm_r x^2## ##dI=(\frac {m_r} {l}dx)x^2## ##I= \int_l^0 (\frac {m_r} {l}dx)x^2 \, dx ## ##I_c.m=\frac {m_r l^2}{3}## ##I_,, = \frac {m_r l^2}{3}+m_p x^2## Given...
  42. J

    Why Did My Torque Sign Change in Rotational Equilibrium?

    See attached for work. I did notice that making the torque from the force of gravity negative I got the right answer, but don't understand what I did wrong (its positive in my solution). i hat cross negative k hat is a positive number after all.
  43. J

    Rotational Equilibrium Problem

    See attached file. Answer is supposed to be 61.25 N, I get 20.09 N.
  44. A

    Rotational Work versus Linear Work

    In the link below, there is a force tangent to a wheel that travels distance Ds. There is also a torque that moved thru an angle. Why do they consider them equal? There are two works, shouldn't they be added together...
  45. narayan821

    Most efficient way to convert rope movement (KE) to rotational KE?

    I've got a moving rope that turns a shaft, which then turns a generator to create electricity. Please point me to a good resource that guides me to perform this efficiently. I would like to maximize the conversion of kinetic energy of the pulled rope system into rotational kinetic energy of the...
  46. T

    Rotational Dynamics - Modeling brake caliper deceleration of a chassis

    I am a junior engineer tasked with modeling the dynamics of a small research UAV after landing. The UAV has 3 tires, 1 on the nose landing gear and 2 on the rear landing gear. The rear tires are equipped with disc brake calipers. My coworker has explained that the simplified model (MODEL 1...
  47. Filip Larsen

    I Rotational invariance of cross product matrix operator

    Given that the normal vector cross product is rotational invariant, that is $$\mathbf R(a\times b) = (\mathbf R a)\times(\mathbf R b),$$ where ##a, b \in \mathbb{R}^3## are two arbitrary (column) vectors and ##\mathbf R## is a 3x3 rotation matrix, and given the cross product matrix operator...
  48. D

    Controlling the rotational speed of a generator

    Hi, I am working on a project that would insert a generator/expander system to a pressurized stream of gas in order to generate electricity. I would like to control the rotational speed of the generator in order to adjust the gas stream flow rate. Would it be possible to control the...
  49. wcjy

    Rotational dynamics and the conservation of energy

    I = Icm + mr^2 I = 0.5 mr^2 + mr^2 I= 3/2 mr^2 By COE, mgh = 0.5(3/2 mr^2)(w^2) g(2r) = 3/4(r^2)(w^2) 8g/3 = rw^2 = v^2 / r v = sqrt( 8gr/3) v=0.511m/s ans: v=0.79m/s
  50. wcjy

    Rotational dynamics: Resolving forces

    Resolving the weight of the cylinder c, i get Mgcosθ (-y) and Mgsinθ (-x) mgsinθ - Fs - T = ma ---(1) (where Fs is frictional force and T is tension) τ = I α (where τ is torque and α is angular acceleration) torque is produced by both tension and frictional force (T-Fs) * r = 0.5 m r^2 α...
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