A tag for questions about rotational motion, including angular velocity and angular acceleration.

learn more… | top users | synonyms

2
votes
1answer
550 views

Equations of motion in 2D [closed]

I'm struggling with a seemingly simple problem in 2D motion. Basically, the question is, given accelerations in $x$ and $y$ ($a_x$ and $a_y$) as well as the angular velocity ($\omega$), how can we ...
2
votes
1answer
385 views

Paradox of the Relativistic Record Player [duplicate]

Possible Duplicate: Invariant spacetime - distance - Circular Motion This is a question that I thought up a few years ago when I was taking mechanics. I asked the professor but didn't really ...
2
votes
5answers
388 views

Instant centre of rotation for two connected gears

The two gears are have the angular velocities $\omega_1$ and $\omega_2$ respectively with respect to $Oxyz$. The task is to determine the angular velocity $\boldsymbol{\omega}$ of the arm $OA$. ...
2
votes
1answer
158 views

Why do some objects tend to change their axis of rotation while rotating?

This question struck me a few minutes back, I was at a table with a pear. It was more narrow than round.I proceeded to rotate this pear in one swift movement. It rotated for a few seconds, and ...
1
vote
2answers
2k views

force applied not on the center of mass

When applying a force outside of the center of mass of the body, the body will get both linear and angular momentum. Right? Does the linear velocity from this force equal to the linear velocity from ...
1
vote
5answers
2k views

Why can mass not be considered concentrated at CM (center of mass) for rotational motion?

Could anyone explain the following expression: Why can mass not be considered concentrated at CM (center of mass) for rotational motion?
1
vote
3answers
268 views

Does circular motion cause centripetal force OR does centripetal force cause circular motion?

Does circular motion cause centripetal force, or does centripetal force cause circular motion, or are they both occurring hand in hand together instantaneously? One more question: If I project a body ...
1
vote
3answers
54 views

Why the similarity in the Equations of Motion for Rotational and Rectilinear Motion?

These are the equations of motion given constant acceleration, for first rectilinear and then rotational motion. Rectilinear Motion: Rotational Motion: While the variables have changed, and the ...
1
vote
2answers
58 views

Why does an ice hockey stick, when thrown on ice always rotate and translate together before coming to rest? Why not only rotate or only translate?

When a hockey stick is thrown on ice it simultaneously rotates and translates before stopping. Friction probably plays the main role here, along with the shape of the stick. I think maybe it is due to ...
1
vote
2answers
295 views

At what point does force stop translating an object and start purely rotating it? [duplicate]

At what point (or distance) from the axis of rotation, does force applied on a rigid body stop translating and purely rotating the body? Can such a point even exist? Does the body always have to ...
1
vote
1answer
327 views

What kind of physical quantity is angular displacement?

Angular Displacement is neither a vector nor a scalar. What type of physical quantity it is? Are there any other examples of that physical quantity?
1
vote
1answer
1k views

If I jump will I land in the same spot? [duplicate]

If I were to jump one meter in the air and hang for one second, would I fall back down in the same spot or would the earth rotate ever so slightly under me, causing me to land a short distance away ...
1
vote
2answers
3k views

Applying angular velocity to a rotation matrix

I have a very simple question. In our project we store an object's orientation as a 3x3 matrix which holds the orthonormal base of that object's local space. For instance if the object is aligned with ...
1
vote
2answers
57 views

When it is usually taken as $\omega=v/r$, why in this particular case $\omega=v/3r$ is taken?

A circular disc of mass m and radius r is set into motion on a horizontal floor with a linear speed v in the forward direction and an angular speed w =v/3r in clockwise direction .Find magnitude of ...
1
vote
1answer
55 views

Why doesn't this differential derivation of the centripetal acceleration formula work?

I wanted to derive centripetal acceleration from scratch and tried using differential equations. But no matter what I did I hit a snag as follows: $\alpha=$ centripetal acceleration $\omega=$ ...
1
vote
5answers
93 views

Doesn't rotational KE of a rolling marble change if there is no friction to provide torque?

The question arise from the following situation: A marble at the border of a uniform bowl begins rolling within it from rest. There is enough friction in the first half the bowl for the marble to not ...
1
vote
2answers
53 views

What is the purpose of the directions for vector quantities such as angular velocity and torque?

Looking at just both angular velocity and torque, many other exhibit this same property. What is the purpose of and usefulness of having a direction that is in the Z-direction? (assuming that, in the ...
1
vote
1answer
103 views

Rotation with axle with unequally sized wheels

https://youtu.be/hwgjMPaKMiA In the above video, I have an assembly of two wheels of unequal radii connected via an axle. Now when we apply an external force anywhere on the axle, we see something ...
1
vote
1answer
44 views

Observations of erratic rotation of asteroids

An asteroid generally has an irregular shape, therefore, one would expect its rotation is quite erratic in some sense. Are there any observational examples?
1
vote
1answer
270 views

If a car moves at a certain speed, how fast is its wheel going?

Say in a given instance a car moves with speed $v$ and consider any wheel of the car. How fast is it going? Is it the case that the center of the wheel moves at the same speed as the car i.e. $v$? Why ...
1
vote
1answer
1k views

Rotational Potential Energy of a Hamster Wheel

Background (unimportant back story)A colleague of mine showed me what i considered flawed statistics, that Internet Explorer had faster Index and array functions than Chrome(we are software ...
1
vote
2answers
2k views

Relative linear velocity of a particle to a rotating object

I am trying to calculate the "relative linear velocity" of a particle moving over a rotating object. According to this paper (section 2.2) I am reading the relative linear velocity is calculated by: ...
1
vote
1answer
50 views

Why will kinetic energy decrease?

Specific situation : A ring of mass M and radius R is rotating about its axis with angular velocity w. Two identical bodies each of mass m are now gently attached at the two ends of a diameter of the ...
1
vote
1answer
64 views

To prove uniqueness of Rotation Tensor [closed]

How can you prove that a rotation tensor which rotates some given vector is a unique tensor? Let's say we have a vector 'a' and we take a tensor product of that vector with some tensor 'Z' such that: ...
1
vote
1answer
35 views

Expressing 3D orientation in alternative to Euler angles for 3D rigid body dynamics

I was unsure whether it would be best to post this in Physics, Maths, or other forums, so please say if this question is suited better elsewhere. I am trying trying to create a physics engine for a ...
1
vote
1answer
252 views

A smaller sphere purely rolling down without slipping over another larger sphere [closed]

In this question we have to find out the angular velocity of the smaller sphere about its own axis at the instant it leaves the surface of the larger sphere and it is given that the smaller sphere is ...
1
vote
4answers
146 views

Why aren't all points on a rolling ball moving?

If a ball is rolling down a hill as shown, what can be said about the points indicated at that particular point in motion? (A) Point A is moving to the left, Point B is at temporarily at ...
1
vote
1answer
146 views

On the no-faster-than-light in special relativity

In the special relativity it is well established that, in the vacuum no one can ever travel faster than light, due to the relativistic velocity addition formula. Recently I saw some silly statement ...
1
vote
1answer
232 views

What role does inertia play in determining how long an egg rotates?

There are two identical eggs boiled egg and raw egg, both are rotated with same angular speed. Which one will come to rest earlier? I have read this question, but it discuss more about friction and ...
1
vote
1answer
372 views

Does rotation increase mass?

If an object is rotated on its axis near the speed of light would its mass increase? Normally if the object was moving (in relationship to the Earth for example) I would agree that its mass would ...
1
vote
1answer
275 views

How to calculate rotational velocity from torque [closed]

Problem as stated: A radio transmission tower has a mass of 80 kg and is 12 m high. The tower is anchored to the ground by a flexible joint at its base, but it is secured by three cables 120 ∘ apart. ...
1
vote
1answer
323 views

Angular acceleration and linear acceleration

I have a small confusion. I learned very recently that all particles of a rotating body have the same angular acceleration but different linear acceleration (same for velocity as well). But how is ...
1
vote
2answers
302 views

Rotational inertia of a ball

This question refers to the solution of problem 12 here. It involves a spherical shell of mass $M$ filled with frictionless fluid of mass $M$ rolling down an inclined plane. (This is problem 12 of ...
1
vote
2answers
649 views

What happens if the earth stops rotating? [duplicate]

I was wondering what would happen to all the components on the surface of the Earth if the Earth suddenly stops rotating but does not stop revolving.
1
vote
1answer
63 views

A pretty dumb question on observation

Very often I have seen, that a bicyclist can balance himself better, while in motion, than he can while at rest(with his legs on the paddles of the bicycle). Now, I know that objects, say, a disc ...
1
vote
1answer
55 views

Inertial navigation system: am I doing it wrong?

I'm trying to develop an inertial navigation system. I can access data from an accelerometer sensor (acceleration on three axes) and gyroscope sensor (angular velocity on three axes). First of all, ...
1
vote
2answers
943 views

Rod sliding on a frictionless surface

A uniform rod$(m,l)$ is standing vertically on a horizontal frictionless surface. Gravity is downwards and uniform. I give its upper end a little push and off it goes. I want to find the Normal Force(...
1
vote
1answer
1k views

Expression for kinetic energy of gas per molecule

The average kinetic energy (KE) per molecule of a gas is $\frac{3}{2}kT$. While finding this we do $$ \text{ Average KE} =\frac{1}{2} M \frac{1}{N}\sum v^2=\frac{3}{2}kT$$ But why do we not add ...
1
vote
1answer
168 views

Determine the velocity and acceleration of the vertex $B$

1) The bent rod $ABCD$ rotates about the line $AD$ whit a constant angular velocity of $90 rad / s$. Determine the velocity and acceleration of the vertex $B$ when the rod is in the position shown in ...
1
vote
1answer
3k views

How is torque equal to moment of inertia times angular acceleration divided by g?

How is the following relation true $$\tau = \large\frac{I}{g} \times \alpha$$ where $\tau$ is torque, $I$ is moment of inertia, $g= 9.8ms^{-2}$, and $\alpha=$ angular acceleration.
1
vote
2answers
334 views

Internal/Rotational angular momentum

I have some difficulties to understand the relation between the internal and the rotational angular momentum of a rigid body which is also known as König's theorem, so what physical intuition lies ...
1
vote
2answers
626 views

Extracting acceleration vector from rotated aircraft

Suppose we have an aircraft with accelerometer measuring accelerations along each axis. It is mounted in a way so it is perpendicular to the plane in all axes (that should be obvious). We also have ...
1
vote
2answers
2k views

What are the expressions for rotational and translational kinetic energies of a system of point particles?

Consider a system of point particles , where the mass of particle $i$ is $\mu_i$ and its position vector is $r_i$. What are the expressions for translational kinetic energy and rotational kinetic ...
1
vote
1answer
1k views

Hollow Wheels Down a Hill

Lets say I have a hoop of mass $M$ and radius $R$. It is rolling down a hill without slipping, so I don't need to worry about friction doing work on it. Lets say the angular speed is $\omega = \frac{...
1
vote
2answers
64 views

How does mass affect slipping of a rolling object?

I experimented by rolling a cylinder down a tube and noticed that by increasing its mass, it's time taken to reach the bottom decreased. Found out that mass doesn't actually affect the time taken, ...
1
vote
1answer
32 views

Rolling motion of a rigid object

I have the situation described in this picture I know the speed of the ball at the top of the loop ($v_{top} = 2.38 m/s$), and I have to demonstrate that the ball does not fall from the track at ...
1
vote
2answers
54 views

Can a system's internal forces change the system's motion?

Let say the motor makes the two rigid body rotate as a same velocity. (they rotate the opposite direction) then the Net force of the motor is 2Fsin(Theta). The acceleration of the motor is 2Fsin(theta)...
1
vote
1answer
43 views

How to find angular velocity of rotated objects in 3D

I am trying to obtain equation for angular velocity of rotated object in 3d. I started with defining yaw, pitch and roll angles. Then I wrote rotation matrices from these angles. As I understand it ...
1
vote
2answers
59 views

Trouble with rotational kinematics

I'm having a bit of trouble with the following homework problem: My thinking is there are only three forces acting on the laundry: the force due to centripetal acceleration, the force due to ...
1
vote
1answer
102 views

How far does the ball travel before pure rolling motion occurs? [closed]

A bowling ball is given an initial speed $V_o = 10 \text{m/s}$ on an alley such that it initially slides without rolling. The coefficient of friction between the ball and the alley is $\mu = 0.06$. ...