# rotational-dynamics's questions - English 1answer

1.671 rotational-dynamics questions.

### Euler's equation for rigid body rotation applied to inertia frame?

According to many rigid body dynamics books, the Euler's equation is expressed in local body frame(principal axes). That is to say the external moment,inertia tensor and angular velocity are all ...

### 3 Does rotation affect impact of a falling ball?

Let's assume a bowling ball is falling to the ground. It will have a certain impact when hitting the ground. Is that impact only depending on the height it's falling from and the weight of the bowling ...

### The teachings of Coriolis [on hold]

Why does the earth not rotate under a hovering helicopter?

### -1 What is difference between rolling, kinetic and static friction? [duplicate]

If there is a toy train on the floor moving linearly then would the friction acting be rolling or static?

### 5 Lagrange: when a potential force, when a generalized force?

Consider the following case of a drum unrolling a mass that is on a massless string wrapped around the drum: According to my professor, here we must consider the mass $m$ being in a gravitational ...

### Angular momentum of the center of gravity of yo-yo

Sorry for my broken English. I am a physics undergrad and only know basic stuff about the subject. Yesterday I was taught about the angular momentum of yo-yo and my prof said that when the yo-yo ...

### -1 Slipping without rolling and acceleration

0 answers, 12 views rotational-dynamics friction torque
The obvious step is to make the torque due to friction equal to the torque due to tension, so Rf = rT. Then, I decided to get make another equation by assuming that the friction is equal to the cosine ...

### Choosing the reference axis in rotational mechanics

In any situation, while applying torque upon any rigid body, can the reference point/axis be any arbitrary point/axis? I mean, is it necessary for the reference axis to be taken only through the ...

### -1 ball spinning in place

Let's say I have a billiard ball. Coefficients of friction are known: μ(rolling) = 0.01 μ(sliding) = 0.2 If we just spin it in place with no velocity. (angular velocity only have z component, ...

### 1 Conditions for Static Equilibrium of Rigid Body

When there are forces acting on a rigid body, the two conditions that has to be satisfied for the body to be in static equilibrium are: 1. The sum of all forces must be zero (translational equilibirum)...

### Friction during ball backspin and overspin

I already know sliding friction of ball on a flat table and rolling resistance of it. How do I know coefficient of friction value when the ball has backspin with some angular velocity $\omega$? And ...

### Flat Earth experiment, but with gyroscope

A man conducted "an experiment" (quotes really, really necessary) to prove that earth is flat. Here's a link. He used a spirit level, set it up before takeoff and expected the level to be tilted after ...

### 4 Rotation and center of mass — A collection of common doubts

There are plenty of similar questions here, but I will nevertheless add another one because I believe this is the ultimate source of confusion (and will probably provide a one-stop solution for future ...

### -1 Principal axes of inertia for periodic systems

We have a 3D periodic crystal and seek to compute the principal axes of inertia. The goal is to have some way to align crystals. (a) Do the principal axes of inertia exist for a periodic system? (b) ...

### 1 Does the Earth volume increase with rotation?

By looking at the rotating car washing brushes, it can be seen that its volume increase with rotation and decrease when it's stopped. So, just for curiosity, would the earth volume decrease if it ...

### -3 Could enough people spin Earth backwards faster than they could run? [duplicate]

So, consider the theoretical situation in which the earth is no longer spinning, and we want to spin it up by running in the opposite direction (Yes, this question was inspired by the Nike commercial)....

### 1 How can a particle in circular motion be in translational motion?

1 answers, 293 views rotational-dynamics angular-velocity
I came across this: If a particle is moving in a circle it is in pure rotational motion about the centre of the circle, while for a moment it may be in pure translational motion about some other ...

### 3 What's the Lagrangian for a freely rotating rod?

This is one of those problems that I thought would be easy, then spent forever on it and realized that I know nothing: A rigid rod of uniform density has mass $M$ and length $L$ and is free to rotate ...

### -1 centre of rotation from a free body diagram of a rigid body? [closed]

Can we find the centre of rotation from a free body diagram of a rigid body? Since the forces can be translated anywhere after adding a corresponding torque/couple and this couple can be moved ...

### 3 Why do we have to take torque due to pseudo force for an accelerating axis?

For e.g. Here, A,B are strings. A was cut. The rod is of length l. Acceleration of center of mass = a and angular acceleration of the rod is alpha. Now if I want to find the net torque about the ...

### -1 Rigid body static friction [duplicate]

Why does the friction of a solid sphere (while rotating and moving) has to be static and not kinetic ,not to slide?

### What is the problem of having an inertia tensor not satisfying the triangle inequality?

It is well known that rigid body inertia tensors are 3 by 3 positive semidefinite matrices, which is the same as saying that their eigenvalues are all non-negative. A little less known is the fact ...

### What type of motion will occur after collision? [duplicate]

I am having some trouble explaining a phenomenon in Newtonian mechanics. If I have a rigid rectangular rod translating with a constant velocity left to right through space that collides with another, ...

### A lever arm-definition question

2 answers, 807 views rotational-dynamics torque
My question is regarding Torque, and specifically the definition of the lever arm. As far as I've understood, the lever arm is the line perpendicular to the line of action to your reference point. ...

### 5 Sum of energy for 2 solids in rotation

I would like to compute the sum of energy of the following case: Two solids are turning (disks). Yellow solid is turning at $w_1$ radians per second around its center of gravity and blue solid is ...

### Pulley inertia momentum of inertia

Considering a pulley with some mass, or some friction, How can its inertia (or momentum of inertia) influence the tension on 1 rope? Which part of the rope is influenced? Before or after the pulley?

### Moment of inertia of a Rod

Imagine a rod inclined like a ladder, to the left, touching a wall. Say, the wall is the Z axis, and the "ladder" is the rod. I want to know how we can calculate the moment of inertia of the rod ...

### 7 General motion of a cone on an inclined surface

Suppose that a solid cone is placed horizontally on an inclined surface and is initially at rest. How will the cone move when it starts motion due to its weight? I know that its motion depends on the ...

### Determine fan sound (dB) based on its rotational speed (RPM)

I am trying to find the sound amplitude or level produced by a fan, knowing its RPM. Is there a simple formula for it? What other parameters does it depend on? Assume I have all the fan properties, ...

### How does precession affect angular momentum?

I have been studying Irodov's problem book. There are a lot of good problems that challenge conceptual knowledge, and so I have to ask somebody for a qualitative answer. I can best describe my ...

### -2 paused point of rotation wheel [closed]

Why is the velocity different for different points on a rolling wheel? In the picture which is in the above linked page, I can see the circle which looks like a set of paused points. But I had known ...

### 1 Relationship between centripetal and angular acceleration?

Regarding circular motion... The way that I know of how to derive the centripetal acceleration is based on the geometrical representation of two instantaneous linear velocities of equal magnitudes on ...

### 1 Finding the radius of curvature of mercury surface in a rotating cylinder [duplicate]

Let us imagine some amount of mercury $\left(\text{Hg}\right)$ contained in a cylinder. It is being rotated about the central axis at a constant angular velocity $ω$, and the system has moment of ...

### 14 Is there any friction between wheel and road?

Human beings invented the wheel to get rid of the friction between the wheel and the road. But were we able to reduce it to zero? Is there any residual friction? This question is about only the ...

### 5 What is a moment?

As a 8th grader I am still a newbie at science and I have problems understanding the forces that I can not imagine and one of these "forces" is the moment. We are told that, $$\text{moment}= Nm$$ ...

### 3 Lagrangian of rotating springs

I'm trying to construct the Lagrangian for the following scenario. A turntable of radius $R$ is rotating at angular velocity $\omega$, maintained by a motor. Two springs with Hooke's constant $k$ are ...

### 1 Why is tangential acceleration always downward in this system?

0 answers, 22 views rotational-dynamics rotation
Point A is rotating about an axis with angular velocity $$w_0=w_i \hat{i} + w_k \hat{k}$$ and has position in the x-z plane $$r=r_i \hat{i} + r_k \hat{k}$$ In addition, the angular velocity vector ...

### 1 How to calculate angle of inclination attained by a weigh balance on unequal loading?

Actually I need to rotate the beam (pivoted at centre) with constant angular velocity using the priciple of mass imbalance. Could anyone suggest what would be rate of decrease of mass in one pan (...

### 1 Circular motion, kinetic friction and tension

Hi: I've read this post: Uniform Circular Motion w/ Tension and Friction and helped me a lot. I have a similar problem: At one end of the rope ($R = 1 m$) is tied a mass ($m = 3 kg$) and the ...

### How to decide if a torque is positive or negative?

In part i, I use $T=I\frac{d^2Q}{dt^2}$ , and get $T=\frac{23g}{150a}\sin Q$ , but the answer is $T=\frac{-23g}{150a}\sin Q$. The only way I can get this answer is if I use $T=-I\frac{d^2Q}{dt^2}$ , ...

### -1 Wheel doing work against gravitational energy [duplicate]

so let's suppose there is a wheel, which rotates thus moving on a flat plane, without any slopes, and the gravitational pull throughout the plane is the same as well. The height of the center of mass ...

### Angular momentum of a rolling cylinder about the point of contact

A cylinder of mass 5 kg and radius 10 cm is moving on a horizontal surface with velocity of centre of mass 5 m/s towards right and angular speed 10 rad/s (clockwise) . Find the angular momentum of the ...