Questions tagged [rotational-kinematics]
A tag for questions about rotational motion, including angular velocity and angular acceleration.
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Why we can move forward in case of backward slipping?
Suppose a wheel which is rolling with backward slipping.
My question is that, if every point which when touch the ground for a short period of time moves in backward direction with respect to ground,...
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Rolling with slipping along an incline [closed]
Here my doubt is about the second question. For the second question I went about using work energy theorem. My thought was that since gravitational and frictional force both will do the same amount of ...
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How much does the Earth lag behind us when we swing?
On a swing, we pull the framework on which the swing hangs. We wriggle our body which has it's effect on the frame, which affects the Earth on it's turn (on it's swing...). It's clear that the ...
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Angular Acceleration of Spinning Body About a Rotating Axis
How would you find the angular acceleration of a body spinning about an axis that is itself rotating? Specifically, how would you find the angular acceleration in question 1.58 of Irodov's physics ...
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Integrating Angular Velocity Vector using Rodrigues' Rotation Formula
My understanding is that Rodrigues Rotation Formula can be used to explicitly compute an exact rotation associated with a constant angular velocity vector over a given time step.
How do you derive the ...
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Serious confusion regarding central concept of torque
I have taken physics, statics, and dynamics, and I have no problem with applying the concept of torque to a problem. But, I just cannot grasp why a force a greater distance away from the axis of ...
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Problems and trignometric generalities
I am practicing physics questions by doing David Morin exercises on classical mechanics. However, I don't understand a particularity of the solution to this problem,
and I think that it's not limited ...
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How do I approximate an angular acceleration vector from a history of orientations?
A rigid body is simulated to move in six degrees of freedom. At every past timestep, I know its displacement vectors $x^{GLOB}$ in the global coordinate frame, as well as 3x3 matrices $R$ that ...
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What is the quantity that is measured in "millijoules per cubic radian"?
Two years back, I asked a similar question, but it was closed as needing details of clarity and then was also deleted. However, I can give a thorough explanation of the translational units and their ...
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How the object rotates?
Why the object actually rotates ?
When I researched about this topic , I have gotten satisfying answer from here:
Why do object rotate at all?
All the atoms and molecules of the object are connected ...
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Why do we use moment of inertia about centre of mass to calculate rotational KE in rolling without slipping?
Say we have a cylinder rolling without slipping on a horizontal plane:
Now, the instantaneous centre of rotation is P, so we can use $ v_A=\omega \ r_{AP}$ to find the linear velocity of the centre ...
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How can I calculate the relative velocity on the surface of a planet that is both rotating and orbiting a star? [closed]
So here is the problem that I'm dealing with:
I thought that I could just subtract the 10000 m/s from the 30000 m/s since they're spinning opposite of each other but that didn't end up giving me the ...
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is $\tau=\frac{dL}{dt}$ true for any arbitrarily changing direction
There is a cylindrically symmetrical top spinning on the ground under the influence of gravity with its tip(i.e. the point on symmetry axis making contact with the ground) at rest. With the tip of the ...
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Angular velocity and axis of rotation
If the angular velocity is along the axis of rotation, then why angular velocity has different components in space and body axis. Let's say $\boldsymbol{\omega}$ is the angular velocity, if it is in ...
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Angular velocity of a particle in uniform circular motion about a general point
This problem was given by our professor.
Consider a particle P executing uniform circular motion wrt the point O with uniform angular velocity $\omega$ anticlockwise whose cordinate is $(2R,0)$ in a ...
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Vehicular Dynamics [closed]
Consider an open differential connected to two wheels on each side. The wheels are flat discs and are 1400 mm apart. This car is making a turn of radius 7 m at a constant angular velocity of 30 ...
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Rate of change of angular speed and tangential acceleration
My textbook gives the following equation
$a_{tan} = \frac{dv}{dt} = \frac{d(r\omega)}{dt} = r\alpha$
Now, what exactly is $\alpha$? I says the rate of change of angular speed, but as it is written, it ...
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How is the angle of the front wheel found in Bicycle Kinematics Model for a Car
My question is, in a 4 wheel model, the front wheels have different angles. To simplify things bicycle model is used. In the bicycle model, there is an imaginary wheel in the middle of the front ...
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Inequivalence of 2nd Moment of Mass and Moment of Inertia
My question is concerned with the difference between two ways of defining the moment of inertia, and how to interpret the difference. Let me begin by saying I understand moments of inertia are ...
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Does it actually make sense to talk about velocity of the point of contact of a wheel rolling without slipping?
I was reading this answer where I saw the following gif:
We can see that when a point becomes point of contact (i.e: touching the ground), the curve of it's motion has a cusp. To my knowledge, a cusp ...
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How much percent of the speed of rotation of the solar surface at the equator is due to frame dragging effect? [closed]
Frame dagging effect is interesting and my particular interest is does this rotation could be compared with the law of motion of planets in a system similar to our Solar system and also can we measure ...
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Kinematics of a rolling disk on a static disk (variation of the Euler disk)
I'm puzzled by the following problem. Consider a simple tilted disk $\mathcal{D}$ of radius 1 (in any unit) rolling without sliding on top of a static horizontal disk $\mathcal{S}$. The normal $\...
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Is $\vec{v} = \frac{2\pi r}{T}$ Referring to Tangential Speed or Velocity?
I seem to be a bit pedantic when it comes to studying physics. Lately, I have been seeing the equation $\vec{v} = \frac{2\pi r}{T}$, which has been causing me trouble. Shouldn't the right expression ...
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Particle revolving in a frustum [closed]
I came across a problem in analysing the motion of a particle revolving in a cone/frustum. We consider a particle that is projected with a velocity $V_o$ along the edge of the frustum. Now we try to ...
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Ratio between linear velocity and angular velocity in a rod thrown by the tip
So imagine a rod that receives an initial impulse acting on its tip. This impulse would cause the rod to translate and rotate about CM. Since the throw is at the tip, the rotational kinetic energy is ...
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Wobble of an unbalanced fan suspended from the ceiling
A fan hangs several feet from the ceiling by a ball-in-socket joint, and it has one fan blade that is heavier than the others.
When you turn on the fan, the additional centrifugal force of the heavy ...
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Physical significance of the angular velocity vector and its projections along different axes
Let's say there is a disk spinning at angular velocity $\omega$. If an observer looks down at the disk directly from the top, he will see the red marker spinning about the center of the disk at ...
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No-circular motion on a turntable
As the title says, I want to model the path of an object sliding on the surface of a turntable, as it is slowly flung off.
The final application of this is , modelling fine material moving along the ...
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How do I determine at what angle to move to intercept another object moving along a circular path?
I came across this issue on my own. This is not a homework problem.
Two people (you and someone else) are running along a circular track, with known positions in relation to each other, and known ...
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Can a planet's rotational axis be determined with a Cavendish torsion beam?
Assuming an arbitrary planet with rotation was explored but for whatever reason (perhaps cloud cover?) the axis of rotation was unknown. Or they needed confirmation... the situation honestly does not ...
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Is force necessary for angular acceleration?
Suppose a body is moving with uniform velocity in the plane along a straight line $y=a$. We can calculate its angular velocity to be $\omega = v \sin^2 \theta / a$, where $\theta$ is the angle ...
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Fault Velocity of centre of mass?
Consider two cases :
The velocity of a small ball coming down a wedge when it reaches the ground is simply (2gh)½ where 'h' is height of wedge .( Given it's initial velocity was zero )
But in case , ...
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Does always angular momentum and angular velocity have the same direction?
I was studying how angular momentum is cancelled when it is transferred directly into the origin of the axis of rotation and during the lecture the professor did something and I was pretty confused.
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What are the equations of motions for a planet in a corotating reference frame?
Imagine standing on the sun and always keeping a polar corotating reference frame.
Start at the perihelion (when earth is closest to the sun). The velocity of the earth is perpendicular to the radius ...
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Meaning of this equation of rotational motion
Tinkering around with rotational movement I ended up with this equation:
$$\omega=\frac{v_t}{r}=\frac{v}{r}\sin\theta = \frac{\sin \theta}{r} \frac{dr}{dt} = \frac{\sin \theta}{r} \frac{dr}{d\phi}\...
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Question about Rotational Kinematics in David Tong's Notes
In the $2$nd page here of David Tong's notes on the Motion of Rigid Bodies, at the bottom there is a claim about the unique existence of a certain time-dependent orthonormal matrix $R(t)$ whose $9$ ...
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Physics of two orbiting masses connected with cable when the cable is cut
The Problem:
Figure 1 - connected masses
In a 2D world without gravity or friction:
Lets say we have two masses, m1 and m2.
They ...
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Confusion regarding angular momentum of a tilted rod
I have a question regarding angular momentum and torque in the following example. This is not a homework problem, I just believe understanding some parts of this particular problem would help me ...
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Relationship between angular and translational velocity on inclined surface
I have been researching about rolling motion and I was calculating a way to predict the translational velocity of the object at the bottom of the incline. I know that the kinetic energy of a cylinder ...
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Frictional wheels without slipping (gear system)
In the figure below it is stated that the friction force should always be greater than the tangential force in order to prevent slipping between two frictional wheels. My question is that if we apply ...
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Kinetic energy of rigid bodies about the center of mass
Suppose, we have some rigid body, that is rotating about some pivot. In this case, we can easily find the kinetic energy, by choosing a random point $P$ on the body. The kinetic energy of the body ( ...
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Torque of a rolling cylinder
I would like to ask the associated net torque equation for this diagram.
Since the tension force is directed counterclockwise, my equation for the torque was
However, the solution to the problem ...
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Maximum theoretical displacement from a ruler catapult
I am considering giving my students the following problem:
Assume we have a ball placed upon a ruler, residing on a table. Now we drop another ball from an height $h$ onto the edge of the ruler. If $...
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What is the relationship between the number of turns of an unwinding pendulum and its radius of motion?
For a pendulum wound around a vertical pole and let go, the largest horizontal distance between the pendulum bob and the pole is r. As the number of times the pendulum is wound around the pole ...
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Kinetics\Biomechanics of throwing a basketball (Elbowjoint)
I'm trying to make a simulation of a person throwing a basketball. My goal is to have at least a shoulder and elbow joint which I can assign with various torques over time to create a motion. When ...
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Resolving angular components in 2D Circular rigid body collision response
I am trying to make a simple 2D physics engine with circles and capsules. So far, I have been able to resolve the velocities of circular bodies after a collision, but I wish to create events like a ...
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Can a particle make a turn in space without accelerating? Does the size of the turn it makes, make a difference?
Is it possible for a particle to have angular velocity but no angular acceleration? Even if the angular velocity does not change, does there always need to be a centripetal / centrifugal acceleration ...
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Angular acceleration related to a time dependent rotation matrix $R(t)$
Let the orientation of a coordinate frame $\{b\}$ w.r.t. a static coordinate frame $\{a\}$ be expressed by a rotation matrix $R_{ab}\in SO(3)$ whose columns represent the coordinates of the unitary ...
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Physics of "Mad Tea Party"
Let's say you have a body rotating about its centre of mass in a rotating frame. But the centre of mass of the body does not coincide with the rotation axis of the rotating frame.
We can often see ...
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What percentage of the universe's energy is rotational kinetic energy?
Obviously there is constant exchange between different forms of energy, so presumably only an average could be estimated, assuming it is not an ill-posed question.
Also, even if a fairly precise ...
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