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

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1answer
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Galactic Rotation of gas clouds

I need to use the formula for the radial velocities of gas clouds due to Galactic rotation together with the assumption of a flat rotation curve ($V$ independent of $R$) to find the Galacto-centric ...
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2answers
61 views

Balancing a pencil

I came across this equation for balancing a pencil while solving some problems: $$ml\ddot { \theta } =mg\theta $$ Where $l=$the length of the pencil, and $\theta$ is the angle it makes with vertical. ...
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0answers
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Torsion Spring Moment Calculation

I'm trying to extend the idea of a translational spring to a rotational spring. Consider a spring that acts on all displacements of a body: $$ \mathbf{F} = \begin{bmatrix} F_x \\ F_y \\ F_z ...
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1answer
49 views

How does the Earth rotate, given that the torque acting on it while revolving is zero?

I've come to understand that the torque acting on the Earth while revolving the Earth is zero. Torque is the force responsible for rotation of a body. So how does the Earth rotate?
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4answers
2k views

Intuition as to why the orientation (of a 3D object) is not a conserved quantity?

Say you start off floating in space, in a fixed position and orientation, with zero linear and angular velocity, with no external forces. So you are a closed mechanical system. By twisting your body ...
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0answers
51 views

Precession due to mountain on Earth [on hold]

I've been stuck on this homework problem, and I could really use some help. My thought process is that when the mountain is added, the Earth will "tip" down in such a way so that the axis of ...
1
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1answer
37 views

Moment of Inertia: uniform rigid rod on smooth plane [closed]

Consider a rod of length $b$ and mass $m$ on a smooth horizontal plane. A force is applied to one end of the rod. What is the acceleration $a$ and angular acceleration $\alpha$ of the other end of ...
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1answer
19 views

Is rolling friction exists only when one body rolls over a plane surface? [closed]

Suppose We have a circular object (A) and at its centre an circular object (B) of the adjusting size is fitted and then the object (B) (axle) is rotated such that it remains in contact wholly with the ...
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1answer
87 views

If a bullet is fired vertically upwards, when it comes back does it fall to the same spot?

What I'm basically asking is that if a body is projected with sufficiently high velocity so that it doesn't escape from the earth's gravitational field but reaches an appreciable height with respect ...
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0answers
19 views

If a molecule collides with a wall, its momentum will change sign. Will its angular momentum also change? [closed]

Consider a diatomic molecule colliding elastically with the wall of a container. We know that its initial angular momentum $p_x$ in the direction normal to the wall will change it sign, so there is a ...
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0answers
19 views

rotational motion of a rigid body [closed]

Find the ratio of radius of gyration of a ring about an axis passing through the ring center, and that of a disc about an axis passing through the disk center, if both the ring and the disc have same ...
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2answers
27 views

Would a black hole's rotational axis precess in orbit around the sun?

The earth rotates, and its axis of rotation precesses due to the gravitational pull of the sun and moon and other planets upon the mass of the earth. If an earth-sized, rotating black hole was in ...
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2answers
55 views

How does a wheel balance itself during circular motion? [duplicate]

A wheel (or any ring of considerable mass) hardly balances itself when it is placed vertically on ground, but when we roll it along the ground it balances itself. What causes this effect? I guess its ...
0
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2answers
253 views

Tricky conceptual question: ball sliding and rolling down incline [on hold]

We all are familiar with the classic ball rolling down the incline exercise in rotational dynamics. Here is quite a tricky conceptual problem: You have an incline of fixed height, but the angle of ...
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1answer
47 views

Determine the value of $g$ with rolling ball

At first, I thought the value of $g$ ($9.8m/s^2$) could be determined simply by placing a ball at the top of a ramp at a known height. The ball was released with no initial velocity, and the final ...
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0answers
22 views

Rotation of Thin street sign

I am attempting to complete a home question in which a shop sign in the shape of a thin rectangle of size p x q (with q being the longer side), and mass m, that rotates about an axis that passes ...
1
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1answer
47 views

Rotation matrix in yo-yo problem?

I need to solve the yo-yo problem not in the normal sense. Instead, I need to include the position vector $r$ and rotation matrix $R$. Assume the yo-yo is rotating in the plane. In the problem yo-yo ...
1
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1answer
48 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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1answer
42 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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3answers
51 views

An object is placed on an inclined plane. Does it roll? [closed]

An object is placed on in inclined plane. There may or may not be friction, your choice. My question is, how do we figure out whether or not it rolls? For example a sphere rolls but a cube doesn't.
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1answer
68 views

How to compute the inertia tensor ${\bf{J}} _{\Omega}$ of a body of revolution

Suppose that $\Omega$ is a body of revolution of the function $y=f(x), a\le x \le b$ around the $x$-axis, where $f(x)>0$ is continuous. How to compute the inertia tensor ${\bf{J}} _{\Omega}$? ...
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2answers
60 views

Second Law for Rotational Motion

Moment of inertia is analogous to mass, and angular acceleration is analogous to linear acceleration. What is analogous quantity to net force? In other words, what is moment of inertia*angular ...
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0answers
25 views

Lagrangian when there are gyroscopic effects

I'm having trouble with this: We have a system that consists of a thin rod (approx. 1-dimensional) and a disk. The rod is free to oscillate in a plane with one of its ending points fixed. The disk is ...
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1answer
45 views

How the torque/moment-of-force can be mathematically defined?

Given the definition of torque/moment-of-force $\mathbf F$ applied in $P$ with respect to the pole $O$ $$ \mathbf M_O=\vec{OP}\times\mathbf F $$ and given that the vectors $\vec{OP}$ and $\mathbf F$ ...
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0answers
53 views

Why is it harder to flip my cell phone about one axis than the other two? [duplicate]

There are three ways (three differenent axis about which) I can flip my cell phone - over the front (like a frontflip), about the center (like a disc of pizza dough being spun by a baker), and over ...
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1answer
97 views

When does the 'standard' angular velocity formula not hold?

I have read that the formula for angular velocity: $$\dot {\vec r}=\vec \omega \times\vec r \tag{1}$$ does not hold in some situations, but the book does not specify what situation so please could you ...
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1answer
39 views

Finding the centripetal force at any random point in a wheel which is rotating as well as translating

If we have a wheel which is decelerating due to friction with acceleration $-A$ and angular acceleration $-\alpha$, and we want to find the acceleration at any point, then we can simply find it using ...
2
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0answers
43 views

Rod rotated by elastic string [closed]

A uniform rod $AB$ of length 2m and mass 1kg, has a mass of 1kg attached at $B$. It can rotate freely about a horizontal axis through $A$. The end $B$ is attached by means of a light elastic string ...
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3answers
44 views

The storage of kinetic energy in a flywhell?

I am reading a book on physics demonstrations and problems, and one of the problems deals with a flywheel which rotates at maximum angular speed. The density of the flywheel is uniform and the ...
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0answers
28 views

Velocity of ball after collision [closed]

I have a question regarding impulse. Suppose at a certain point of time ball has velocity $\mathbf{v}\cos\theta$ in horizontal direction and $\mathbf{v}\sin\theta$ in vertical direction (downwards) ...
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0answers
62 views

Boiled egg vs raw egg moment of inertia

I know that the acceleration of some body rolling down an incline with fixed inclination goes as $1/(k+1)$ where the moment of inertia of the body is $kmr^2$. I am trying to decide whether a raw egg ...
2
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0answers
54 views

How to get from momentum to force

Situation: I have a solid object (black) attached to a rod (blue) as shown below: The rod is fixed at the top. The solid object is a cylinder as shown, with a rate of rotation ...
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1answer
20 views

Pure Rolling from a stationary surface onto a moving surface

Suppose a sphere rolls without slipping on horizontal stationary ground. Now, suppose the sphere rolls onto a surface which is moving at some velocity with respect to the previous stationary ground. ...
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2answers
38 views

Can center of mass move without any force?

For instance, consider a weight on one end of the ring. Assume that the ring has negligible mass compared to the weight. When the weight splits into two, moves around the ring and recombines at the ...
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2answers
62 views

Acceleration of ball rolling down incline

Suppose you have some object (which can roll like a ball,cylinder,wheel,etc) rolling down an incline without slipping (moment of intertia $I=kmr^2$. I want to find the accleration of the ball as it ...
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0answers
63 views

Why golf balls travel faster if they spin?

From the book I have been given to read I found that balls spin due to the centripetal force but i am confused about how exactly do the resultant force causes it to spin and move forward about the ...
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0answers
51 views

How would an observer feel the Einstein Thirring Lense Effect?

The Einstein Thirring Lense Effect, also known as Frame Dragging, is what happens when cellestial bodies have rotation. It states that when a body of mass is rotating around an axis it drags space and ...
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2answers
133 views

Rolling as pure rotation

In my book the following statement was written and I didn't understand it well. Can anyone explain it in a more simple way? Figure 11-6 suggests another way to look at the rolling motion of a ...
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3answers
57 views

Newton's Second law of Rotation

In my book (Halliday Resnick Walker) there is a solved example which is as follows There is a uniform disk with mass $M$ = 2.5kg and radius $R$ = 20cm, mounted on a fixed horizontal axle. A block ...
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1answer
43 views

How to calculate time from different instantaneous velocities and accelerations?

I have a closing door, that moves from angle 75 to angle 5. Torque acting on that door at each angle is known -of course differs at each angle- I want to calculate the time required for that door to ...
2
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2answers
61 views

How's equilibrium possible here?

Here's the question.......Two point masses $m$ and $2m$ are attached at each end of a light rod. The rod is pivoted at the center and is free to move in a vertical plane. Then find the angle $A$ when ...
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1answer
29 views

Is the distance involved in calculating angular momentum to an axis or a point?

I'm a high school student.I still don't really understand angular momentum and moment of inertia. I know the moment of inertia of a point mass is defined as $mr^2$. For any other shape, we integrate ...
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1answer
46 views

Why to use radius of gyration? [closed]

I know the definition of radius of gyration. But don't know why does it mean? What are the importances of it? Is it similiar to centre of mass?
2
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2answers
142 views

Why doesn't the ball have rotational energy after it leaves the ramp?

I am having trouble solving #13 from the 2010 F=MA contest: A ball of mass $M$ and radius $R$ has a moment of inertia of $I = \frac{2}{5}MR^2$. The ball is released from rest and rolls down the ...
0
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1answer
53 views

Is work done in rolling friction?

I am confused by rolling friction. Suppose you have a cylinder rolling which starts at rest at the top of an incline plane and begins to roll down the plane without slipping. Is work done by the ...
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0answers
39 views

How to solve this rotational mechanics problem? [duplicate]

I was doing this problem for self study in rotational dynamics: Two discs are mounted on thin, lightweight rods oriented through their centers and normal to the discs. These axles are constrained ...
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2answers
60 views

Torque at a disc sandwiched between two rotating discs

I have a question in my mind regarding torque transfer taking place in the current situation. There are three rotation elements A, B & C as shown in the figure. The rotating element A is ...
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3answers
119 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 ...
3
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1answer
58 views

Changing Earth angle of revolution

As a follow-up to the two previous questions What is the scientific reason for the inclination of earth's rotation axis? and How much effort would be required to fix the Earth's rotation? ...
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1answer
63 views

Transfer between translative KE and rotational KE in a rigid body

I have been inspired by some sci-fi cannons that seem to operate by initially spinning up a projectile inside the cannon, and then suddenly firing the projectile out at high speed. Now, I am wondering ...