Questions tagged [rotational-kinematics]
A tag for questions about rotational motion, including angular velocity and angular acceleration.
1,293
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Is it possible in principle, to analyze problems in rotational mechanics using force and mass, instead of torque and the moment of inertia?
Suppose we are studying the case of uniform circular motion. The analysis of such motion is usually done using Newton's second law as $ma=m v^2/r$. Even when the motion isn't purely circular, like the ...
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How long would it take for down becoming the opposite on earth?
Sorry if the question is unclear, I will try to explain it better.
Let's say that I am standing still somewhere on the planet and I say while pointing at my feet :"Down is this way", how ...
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Reasons for using Angular momentum, Torque and Moment of inertia to describe rotational motion
In order to describe rotational motion, we usually ditch the familiar concepts of force, linear momentum and mass, and use instead their moments to describe the motion. Is it just because it makes our ...
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Tangential acceleration of a two-dimensional rotating mass point [closed]
An object moves on the trajectory
$$\vec{r}(t)=c\cdot\big(\theta t,\sin{(\theta t)}\big).$$
I know how to calculate the vector of acceleration (second derivative of $\vec{r}$).
$$\vec{a}(t)=c\cdot\big(...
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Does the centrifugal force of a rotating object acts at this same rotating object?
when rotating an object by a string a centripetal force from the string will act at the object towards the center and by Newton's 3rd law an opposite force will act at the string by the object . Then ...
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Determining the minimum amount of torque to make wheels start rolling
Context: I am building a cart with mass m (including the cart and the payload) that has 4 wheels. The 2 back wheels will be driven by motors. I am trying to determine the minimum amount of torque ...
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Why is the direction of friction different in case of rolling on plane surface and on an inclined plane?
I was studying the rolling of spherical objects on plane surfaces and inclined planes. I had doubts about the direction of friction in both cases.
Case 1-
In the first case i.e. rolling on the plane ...
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Tangential velocity - Spherical coordinates
In a spherical coordinates system ($r$, $\theta$, $\phi$ ), assuming an angular rotation $\omega_z$ around the z-axis, the tangential velocity of a point can be expressed as:
$$V_x = -\omega_z R \sin\...
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Elliptic motion [closed]
I'm given the following motion:
$$x(t)=A\cos(\omega t)\\y(t)=B\sin(\omega t)$$
I'm asked to describe what kind of motion it is and other things. The thing that puzzles me is that my first approach was ...
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Vector cross product formula without a second term (Spiegel, Theoretical Mechanics)
In Spiegel's Outline Of Theoretical Mechanics (more precisely in the Moving Coordinate Systems chapter, § "Derivative Operators") I find (both in the 1968 and the 1977 edition) the following ...
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The impact of mass distribution on time taken for a cylinder to roll down a ramp
I am carrying out an experiment to test out the impact of mass distribution on time taken for a cylinder to roll down a ramp. I have kept the overall mass of the cylinder constant, as well as the ...
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Work done when decreasing the radius of a rotating object [closed]
This is 4.4 in Taylor's classical mechanics textbook.
"A particle of mass $m$ is moving on a frictionless horizontal table and is attached to a massless string, whose other end passes through a ...
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Resultant velocity in rolling motion
Why is the resultant velocity of a
particle inside a body undergoing rolling without slipping always perpendicular to the line segment connecting it and the instantaneous axis of rotation?
$P_2V_2$ ...
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Finding Average Acceleration with only given angle [closed]
A car enters a curve in the road with a speed of 32 m/s and emerges from this curve 4 s later with the same speed. However, the direction of the velocity changes by 150 degrees during this time.
What ...
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Does angular velocity obey vector addition?
Suppose I take a water bottle and impart two angular velocities on it simultaneously, i.e.
along the axis of the bottle
of the axis of the bottle itself about another axis perpendicular to it
what ...
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Predicting future position given linear velocity and angular velocity at $t=0$
I'm working on predicting the path of a point in 3D space for a game; at any moment, I'll have the point's linear velocity vector $\vec v (x, y, z)$ in m/s, and angular velocity $\vec\omega$ in rads/s ...
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Equilibrium between spring and centrifugal force
I was doing a problem regarding balancing springs in rotation about an axis with a respective centrifugal force.
Axis of rotation goes through a human. Springs starts 1 meter away from the axis of ...
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Mapping of 6DOF Movement in Space to 2DOF (Kinematics + Dynamics)
I need to describe a 6DOF movement in space with 2 axes, Azimuth and Elevation (Inner and Outer Gimbal). The 6DOF movement is a platform disturbance to a stabilization system. The disturbance has 3-...
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Centrifugal Force & Rotating Frames [duplicate]
In Thornton & Marion's Classical Dynamics, the following relation is given for the rate of change of an objects position in the two coordinate systems (according to the picture shown at the bottom)...
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Where should the reference point be considered during torque measurement?
This is an extremely silly and wierd question.
https://en.wikipedia.org/wiki/Varignon%27s_theorem_(mechanics)
While reading about Varignon's Theorem in wikipedia I noticed this sentence,
"If ...
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Will a cylinder/sphere roll on a rope if half of it is surrounded by rope and one end of the rope being pulled?
Rolling a cylinder using a rope having one end fixed and another end mobile
Will the cylinder/sphere roll as per the conditions mentioned in the above question(link)? Are there any additional ...
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Hurricane - trajectory in a logarithmic spiral
Let $f : [0,\infty[ \longrightarrow [0,\infty[$ be a given function and consider a particle on the plane such that
the particle starts at point $p_0$ at time $t=0$,
its trajectory $t \mapsto p_t $ is ...
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Rotation in 3D space
Suppose a body that rotates around an axis. But the axis also rotates. Now, the axis of the rotation of the axis also rotates, and so on. How far we can go with it? Can it be extended to infinity like ...
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Is moving into a rotating frame a Galilean transformation?
In classical mechanics, we know that laws of physics are invariant in Galilean transformations of the form:
$$ x' = x -vt$$
My question is does shifting to rotating frame also count as a Galilean ...
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What is the tangential velocity of a cylinder which is moving with a translational/ linear velocity (of center of mass)? [closed]
Let a cylinder is made to roll in such a way that the velocity of its center of mass is $v$ $m/s$. Are the particles of its surface supposed to move with equivalent tangential velocity? It is to be ...
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Does rotational kinetic energy convert to translational energy when an spinning/revolving object is released in space/vacuum/air(no resistance)?
If an object (symmetric and circular/cylindrical/spherical) is made to roll on a surface and is made to fall from the edge of the surface, will its rotational kinetic energy convert to translational ...
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Newton's second law for rotating body with changing mass
Newton's second law for a body with changing mass given as $$F=ma + \frac{dm}{dt}v$$ I need the version for rotational motion. By inspection, it seems that it would be $$\tau = I\alpha + \frac{dI}{dt}\...
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An object on top of a rotating mass like earth
Why do objects fall down in same place on the rotating earth? I get that newton's first law is the reason an object falling on a high speed train will maintain the same velocity as a train and ...
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3
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Centripetal force in circular motion
We know that when a body moves in a circle,the acceleration which is responsible for changing the velocity of the body is centripetal acceleration which acts toward the center and the force which is ...
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What is the conversion ratio of linear to angular momentum when a ball hits a rod in space?
If the ball hits the rod at 90 degrees then the rod will start spinning, while also following the original trajectory of the ball. On what factors does the ratio between the two types of momentum ...
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Speed of light in a rotating disc (tangential) [duplicate]
My son came with this "idea" to "exceed the speed of light" (he is still in school):
Imagine a disc of radius $R$ that is rotating so fast [with angular speed $\omega$ so large] ...
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Use of net acceleration in circular motion
We know there are two types of accelaration in circular motion, one is centripetal acceleration and the other one is tangential acceleration. The resultant of these two is the net acceleration $a$. ...
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Center of wheel travels the length of circumference in one revolution
I asked the same question first on the mathematics forum here.
I was wondering if there is a more mathematical/rigorous way of seeing
that the wheel/circle/its center travels the length of wheel's
...
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Spinning a rod in relativistic speed
This is a random question that just comes into my mind.
Say you have a rod with a length of 6 x $10^8$ m and I spin it at its mid point at 1 rad/s. By classical mechanics the end of the rod would have ...
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Infinitesimal displacement when rotating a vector
I found this in a kinematics book and this section is on angular velocity, and since no diagram is given I assumed that they are describing something that looks like this:
Consider an infinitesimal ...
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Will I change the RPM of the front wheel of my bike (when lifting it off the ground) just by moving the handlebar back and forth?
I lift the front wheel of my bike off the ground and make it spin. I turn the handlebars right-left-right-left.
I feel the resistance of moving the handlebar back and forth. The faster the wheel spins ...
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Is it possible to calculate angular acceleration from a measured linear acceleration?
I am trying to use an accelerometer to measure the angular acceleration of a robotic arm.
From rigid body kinematics, the following relation is known
\begin{align*} {^{i} {\boldsymbol{a}}_m} & = {^...
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Work done when a ball is rolled uphill vs downhill
There is no change in rotational or linear velocity during the process.
Can you explain the work done by the person rolling the ball, in the two cases, ideally. I would prefer an explanation without ...
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In Atwood machines, is the direction of the acceleration an observational fact or can be deduced mathematically?
In Atwood machines type problems, we set one block heavier than the other. Then we usually "know" the direction of rotation of the pulley and the direction of acceleration based on the ...
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Help with derivation of Kinetic Energy of N point masses
There are $N$ point masses as shown in image each with mass $m_i$ and velocity $v_i$.
We need to find the Kinetic Energy of the system. Here is the proof attached I have some doubt in it.
The doubt ...
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Centrifugal force, Newton's third law and increasing radius?
Say there are two masses $m$ and $M$ that are independent. They are travelling in a circular path around the same centre with the same angular velocity. For mass $M$, centrifugal force is larger and ...
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Rigorous proof that a net force of zero guarantees zero linear acceleration in rigid bodies
I've never found a rigorous proof of this fact.
The center of mass' acceleration is not necessarily the linear acceleration, specially if the body is attached to a pin or another geometric constrain, ...
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The relationship between velocity of centre of mass and angular velocity of a rigid body
Consider a rotating object with mass $m$, moment of inertia $I$, along an inclined plane of vertical height $h$. Then simply speaking the following conservation law holds.
$$\frac{1}{2}(mv_{CM}^2+I\...
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Rolling motion on a frictionless surface [duplicate]
I had the following question:
You are on a frictionless surface. How can you move horizontally if no horizontal force is exerted by pushing against the surface?
$a.$ By rolling your body on the ...
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Centripetal force equation doubt
In a centrifuge, $a_c$ should be constant. If $m$ increases, the $r$ will increase in order to maintain a constant $a_c$.
Constant centrieptal acceleration is given by
$a_c={ v^2 \over r}$
and $a_c = ...
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3
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What is the effect of a tangential force on a rigid body in terms of kinetic energy? [duplicate]
Let's take into consideration a sphere. We apply a force F tangent to the sphere.
We know that the linear acceleration of that sphere will be equal to F/m where m is the total mass of the sphere.
Then ...
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1
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Would this be a correct explanation on denser molecules end up further away from axis of rotation in a centrifuge?
Here's my following explanation for why denser molecules end up further away from axis of rotation in a centrifuge (i got this from my other account on physics stack exchange - yug)
A centrifuge ...
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Rotational Motion (Axe and Grindstone) [closed]
You have a grindstone that is 90.0kg, has a radius of 0.34m and is turning st 90 rpm. You press a steel axe against it with a radial force of 20.0N. Assuming that the kinetic coefficient of friction ...
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Need for velocity as rate of change of displacement
Think of the following 2 cases:
An object is in rotation. Take a quarter arc of a circle. The initial and final points of that quarter arc are $A$ and $B$. if we have the arc length as $l$ and time ...
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Linear variables in circular motion
The following is a really basic problem. I am not interested in the solution rather why the particular solution mentioned below works in all general cases:
Let's imagine a person is running through a ...