A tag for questions about the mechanical interactions of rotating objects, including torque and angular momentum.

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69 views

Angular momentum of rolling sphere [closed]

A sphere of uniform density $\rho$ and radius $r$ is rolling without slipping on a perfectly flat surface. It is moving in a perfectly straight line and its axis of rotation is parallel to the plane ...
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3answers
42 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 ...
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4answers
127 views

Spinning disk touches stationary disk [closed]

Suppose we have a solid disk of mass $M$ and radius $R$ that is spinning at an angular velocity of $\omega_0$ about an axis going out its cm. It is brought to touch a stationary disk of mass $m$ and ...
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2answers
127 views

Rotational speed of a planet [closed]

Is there a way to calculate the rotational speed (or day length) of a planet? If not then what are the factors? I mean what affects the speed? Is it just the distance from Sun (like period of a ...
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1answer
72 views

Potential Energy Problem

We know that, the potential energy of a particle is $U= mgh$ where $h$ is the height from the zero potential point. But what I have found in Resnick's Fundamental of physics book is that they ...
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1answer
135 views

When will the pringles can fall?

When I'm pushing a tall, cylindrical object stood on its end (like a Pringles can) I can push it near its bottom, and it will slide forwards, or push it near the top, and it will topple over. So, ...
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2answers
148 views

Can we get energy from the Earth's rotation?

Is there any way to harvest large amounts of energy from the Earth's rotation?
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2answers
302 views

If a ball spinning on a rod hits another ball, what is conserved linear or angular momentum?

Suppose a 1-kg ball A is fixed to a spoke 0.2 m long, which is attached to an axle so that the ball can rotate (v=10m/s, KE=50J, $\omega$=50 rps, L=2, p=0) Now, there is a second ball B (m=1kg), ...
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2answers
2k views

Derivation of Euler's equations for rigid body rotation

Sorry for using this image, but I thought this was the most convenient way of asking this question. Please zoom in. I do not understand from the line, "Now, in the body frame $T = (T_{x'}, T_{y'}, ...
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1answer
848 views

Moment of Inertia and Rotational Dynamics? [closed]

I'm having problems with the intuition behind the Parallel axis theorem and the Perpendicular axis theorem. I'm self studying Mechanics for the British Curriculum but, the book I've is missing the ...
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1answer
715 views

What is the friction between cylinder and wall (ground)?

A hollow cylinder (radius $R$) is rolling against the wall at angular speed $\omega$. The coefficient of friction between the cylinder and the wall(ground) is $\mu$. After how many rotations the ...
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1answer
471 views

Independence of angular momentum with respect to origin for rotation about center of mass

Why is angular momentum for rotation about the center of mass independent of origin of the coordinate system?
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1answer
2k views

Kinetic Energy And Rotational Motion

The problem is, "A metal can containing condensed mushroom soup has mass 220 g, height 11.0 cm and diameter 6.38 cm. It is placed at rest on its side at the top of a 3.00-m-long incline that is at ...
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3answers
3k views

Centripetal force of a rotating rigid body?

Consider someone pushing a roundabout in a playground. Initially the roundabout is stationary, but when it is pushed, it rotates with increasing rotational speed. The force of the push is ...
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3answers
65 views

Moment of inertia of 4 particle system

Four particles are connected by rigid rods of negligible mass. The origin is at the center of the rectangle. The system rotates in the $xy$ plane about the z axis with an angular speed of $6$ rad/s. ...
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1answer
56 views

How I think about rolling [closed]

Below, I have written how I think about rolling. I wish to know if my idea as to how it works is correct. Consider a rigid ball on a plane which has considerable friction. If you push the ball ...
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1answer
101 views

Conservation of angular momentum during rolling

A disk having initial angular velocity $\omega$ is gently placed on a rough horizontal surface. What is the angular velocity of rotation when pure rolling starts? I've tried applying conservation ...
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2answers
49 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 ...
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2answers
237 views

How does this spool have an angular acceleration opposite to its acceleration?

Consider this spool. It rests on a rough horizontal force. The green lines are the ground, and a line parallel to the ground. The spool is pulled without sliding by the thread (with tension T), with ...
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1answer
80 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 ...
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1answer
150 views

How is angular momentum conserved?

A uniform vertical turntable (mass M and radius R center O) is at rest on the xy plane and is mounted on a frictionless axle, which lies along the vertical z axis. I throw a lump of putty mass m with ...
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3answers
115 views

Will computer fan rotate slower if one makes impeller heavier?

Imagine that we replace plastic fan impeller with identical metal impeller (same form, heavier weight). Would maximum fan speed decrease? Common sense suggests that air resistance and bearing ...
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3answers
113 views

Can the anti-torque of a motor be used to spin a space vehicle about it's axis?

Imagine an electric motor together with its power supply in space. What exactly will happen to it if it is suddenly powered? Will it spin about its axis, or it will experience no motion relative to an ...
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2answers
72 views

Compute the inertial tensor and then solve the equation? [closed]

If the $J_{\Omega}$ is the following matrix, which is solved by ja72 in How to compute the inertia tensor ${\bf{J}} _{\Omega}$ of a body of revolution: $${\bf J} = \rho\, \begin{bmatrix} ...
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3answers
248 views

$F=ma$ contest problem on angular momentum [closed]

Problem #25 from the 2009 $F=ma$ contest: Two discs are mounted on thin, lightweight rods oriented through their centers and normal to the discs. These axles are constrained to be vertical at all ...
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2answers
165 views

Flipping a bottle

I tried to do this experiment recently at school and my house. I started the experiment by having three same type of bottles with the labels A,B and C. Bottle A has been fully filled with water, ...
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3answers
83 views

Problem in understanding the process of calculating the rotational inertia

As we know, rotational inertia is the mass-equivalent in rotation. For a discrete body, it is measured as $$I = \sum m_i{r_i}^2 $$ . But when a continuous body comes, $$I = \int r^2 .dm$$ which ...
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2answers
226 views

Why does the Earth rotate on its axis?

I know that the earth moves around the sun because of the gravity force, because the spacetime around the sun is curved. But why does the earth rotate on its axis, and which parameters can affect ...
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1answer
127 views

Gravitational Potential Energy to Kinetic Energy

When a yo-yo is released from a height $h$, the gravitational potential energy is converted to kinetic energy. However, the yo-yo obviously has less acceleration than $g$, $9.8\frac{m}{s}$. This means ...
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1answer
717 views

Toppling of a cylinder on a block

A uniform cylinder rests on a cart.The height and diameter is given.coefficient of static friction is given.How can i find the minimum acceleration of block such that the block topples? Morever what ...
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3answers
2k views

Work Done by Rockets in Orbital Motion

A weather satellite ($m_s = 4350$ kg) is in a stable circular orbit around the Earth ($m_E = 5.97 \cdot 10^{24}$ kg). It completes an orbit once every 2 and a half hours. (I'm sure about these 2 ...
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2answers
79 views

Centripetal force: if radius decreases, does ANGULAR or TANGENTIAL velocity change?

Having conceptual trouble with this aspect of centripetal force. Say we have a puck on a frictionless table attached to a string that I am holding through a small hole, so that the puck moves in a ...
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1answer
32 views

Conservation of momentum (angular and translational) [closed]

A ring of radius $R$ and mass $M$ lies on its side on a frictionless table. A bug of mass $m$ rests on the ring. The bug starts walking on the ring with constant speed $v$ relative to the ring. ...
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1answer
89 views

Spinning a string with a mass on the end. What makes the mass rotate parallel to the ground? [closed]

Say you use your hand to rotate a string with a mass attached to the end. The string will first become taunt and then the mass and string will move upwards until they are spinning parallel to the ...
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1answer
41 views

Parallel axis theorem and Koenig theorem for angular momentum

Are the parallel axis theorem and the Koenig theorem for angular momentum linked with each other in rigid body dynamics? The parallel axis theorem states that $$I_{z}=I_{cm}+ma^2$$ Koenig theorem ...
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3answers
76 views

Why doesn't a swing make a full revolution on a swingset in a park? [closed]

I'm familiar with the concept of swinging of a swing in a park, but I'm confused why it doesn't it swing at a complete circle around the center bar?
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2answers
37 views

Definition of translational , rotational , rolling motion

What are the exact definitions of pure translational , pure rotational and rolling motion ? I am a class 11th student ... I find it difficult to exactly make a difference between translational , ...
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2answers
107 views

Difference between potential centrifugal energy and rotational/kinetic energy

I'm having troubles to understand the difference between kinetic energy and potential centrifugal energy in some situations. I make an example where I am confused. A object moves on a rod attached ...
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2answers
53 views

Does orbital motion cause rotation?

Assume the moon was flying freely in space, and not rotating at all. If if then happened to pass earth at just the right distance and velocity to fall into orbit, would its absolute rotation be ...
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1answer
63 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: ...
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1answer
90 views

Gyroscope precession

I have a system diagrammed and explained in the image below. Experimentally I believe the wheel will rotate around the pivot point where the cable is attached in a counter-clock motion if ...
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1answer
30 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 ...
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1answer
151 views

How to make a body rotate about a line that does not go through its center of mass by applying external torques

In space, is it possible to make a body rotate a point that does not go through its center of mass by applying external torques?
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2answers
1k views

Will increased weight slow a pendulum?

When a pendulum is swinging, if you could instantly add significant weight to the bob without altering it in any other way, will that weight increase drag and cause the pendulum to move to equilibrium ...
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1answer
254 views

Moment of Inertia Calculation [closed]

A uniform disc has centre O, radius a and mass 2m. It is free to rotate in a vertical plane about a horizontal axis through O. A particle P of mass m is placed on the highest point of the rough edge ...
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2answers
80 views

What should we do If we wanted to increase the angular velocity of a planet? [duplicate]

We could hit it with really fast objects, but could we manipulate the orbit of a large satellite to speed up its rotation? What would be the easiest way?
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1answer
112 views

Angular velocity and instantaneous rotation axis

Let's suppose that we have a cylinder of moment of inertia $I$ rolling on the floor without sliding, moving with linear velocity $v$ and rotating around an axis passing through the center of mass with ...
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1answer
102 views

Running Euler's disk in a superfluid

I was considering the toy Euler's Disk, a video can be found here: http://www.youtube.com/watch?v=mVl2CBG_h2s I was interested in understanding the behavior of the disk particularly in vacuum and in ...
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1answer
119 views

Disk and Ball on a smooth surface [closed]

A uniform disk of mass $\text{2m}$ and radius $\text{R}$ is placed freely on a smooth surface as shown in the figure. A particle of mass $\text{m}$ is connected to the circumference of the disc with a ...
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4answers
235 views

Rotation systems. Problem interpreting an equation

In this equation: $$ \mathbf a_i\overset{\rm def}{=}\left(\frac{d^2\mathbf r}{dt^2}\right)_i=\left(\frac{d\mathbf ...