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

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1answer
248 views

Calculating the time to stop a wheel with friction [closed]

I'm trying to solve the following problem, but i have no idea how to begin. A wheel of mass $M$, radius of gyration $k$, spins smoothly on a fixed horizontal axle of radius a which passes through ...
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2answers
115 views

Eulerian Angles — Why three rotations can transform fixed frame into body frame?

"In general, if we restrict ourselves to rotations about one of the Cartesian axes, three successive rotations are required to transform the fixed frame into the body frame" The origin of our fixed ...
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1answer
67 views

Ask an equation to solve the next location of an object?

It is a long time that I have not learnt physics. But now I really need an equation to solve a problem. I appreciate physicists give me a little hint. Here is a object on the desk without friction. ...
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1answer
215 views

Newton's second law for rotation

Can the second law of motion for rotation, $\vec{\tau}=I \vec{\alpha}$, be used for any axis? Is there any case that acceleration $\vec{\alpha}$ is not in the direction of applied torque ...
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1answer
330 views

Question regarding mass hanging from center edge of rotating disc

So, say you have a free to rotate disc, assuming no external torques, and you have a spool, radius 7.93 mm, attached to its centre. Say the spool has a string attached to a point on its edge and ...
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3answers
1k views

Why does a bicycle (without any support of stand) falls down being at rest, but not under motion? [duplicate]

I have always seen a bicycle not standing without any support, it either falls down to the right or to the left, may even to some other direction. But,the same two wheeler when under motion,moves ...
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1answer
1k views

Calculating torque in 3D?

Say you have a sphere, and you have several torque vectors acting on it, all at different points. Say you have the vector (6i + 3j + 5k) originating from point A, and the vector (3i + 1j + 9k) ...
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1answer
795 views

Component of angular velocity along an axis inclined at $\theta$

If an arbitrary rigid body rotates with angular velocity $\omega_0$ about some axis, can it be said that the body will rotate with an angular velocity $\omega_0 \cos(\theta)$ about an axis which is at ...
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1answer
314 views

A rod of length $L$ & mass $M$ is rotating in a circle about one end then calculate tension in the rod at a distance $x$ from the support

A rod of length L & mass M is rotating in a circle about one end then calculate tension in the rod at a distance 'x' from the support ? For its solution why should we take mass of L-x portion of ...
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1answer
350 views

Physics of the point of contact for a spinning top

I understand how spinning tops don't tip over, cf. e.g. this and this Phys.SE questions. What I'm more interested is in identifying the factors that determine the direction the spinning top moves to? ...
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1answer
800 views

Non-commutative property of rotation

Addition of angles are non-commutative in three dimensions. Hence some other angular vector quantities like angular velocity, momentum become non-commutative. What is the physical significance of this ...
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3answers
1k views

Aircraft Level Flight Trajectory

An aircraft climbs to 15000 feet and enters 'level flight' phase. My basic knowledge of physics says that forces on the aircraft at this time are balanced - as seen in this diagram. Would an ...
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1answer
70 views

Rotation of diatomic homonuclear molecule

I know that the rotation energy of a diatomic homonuclear molecule is $E_{Rot}=\frac{\hbar J(J+1)}{R^2 M}$. Does the axis of rotation depend on $J$? With respect to which axis does the molecule for ...
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1answer
351 views

What controls whether a ball will skid or roll?

A billard ball is struck with a cue. The line of action of the applied impulse is horizontal and passes through the center of the ball. The initial velocity $v_0$ of the ball, its radius $R$, its mass ...
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1answer
463 views

What techniques can be used to analyze a rod rotating about the edge of a table?

A uniform rod of length $4x$ is rotating about the edge $O$ of the table. (The rod does not fall off the table.) The centre of mass $G$ of the rod is distance $x$ away from $O$. The rod is making ...
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1answer
2k views

Calculation for force generated by a rotating rectangular blade

When trying to calculate the lift force generated by a simple rectangular blade, I've found the following equation: $$F = \omega^2 L^2 l\rho\sin^2\phi$$ in which $\omega$ is the angular velocity, $L$ ...
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1answer
637 views

Problem based on Rotational Motion [closed]

A spool of mass $\mathsf m$ and inner radius $\mathsf r$ and outer radius $\mathsf{2r}$, having moment of inertia $\Large\mathsf{\frac{mr^2}{2}}$ is made to roll without sliding on a rough ...
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2answers
7k views

Would a light or a heavy ball roll fastest down a slope?

A small, light ball and a larger, heavier ball are released from the top of a slope. Which will move further? which will come down faster?
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1answer
314 views

Artificial Gravity - Spinning Station Questions II

In an answer to Artificial Gravity - Spinning Station Questions Vintage wrote: A theoretical space station of radius 900 meters, doing a complete rotation every 60 seconds (in order to generate ...
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2answers
717 views

How are Euler's laws of motion applied to gyroscopes?

Euler's laws of motion for a distributed mass are: $$F = \frac{d}{dt} MV_{cm},\ N = \frac{d}{dt} L$$ $F$ are the sum of the external forces, $M$ the total mass, $V_{cm}$ the velocity of the centre ...
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1answer
223 views

Top spun up with string under tension problem [duplicate]

Possible Duplicate: Homework about spinning top I have a top with an unknown mass. It has a moment of inertia of 4.00 * 10^-7 kgm^2 a string is wrapped around the top and pulls it so that ...
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1answer
2k views

Finding angular acceleration from torque

We have to analyze this video Givens: An applied net torque due to the wind on the windmill is equal to 1500 N*m. Each (of the 3) propeller props weighs approximately 45 Kg and has a Moment of ...
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1answer
50 views

Reduction of Earth's Rotation due to increase in humidity

I came to know that, moon is moving away from earth, resulting reduction of Earth's rotation. Similarly, if Earth's humidity increases, water vapor will be move up to the air from water sources, will ...
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1answer
25 views

How far does a ball thrown over a surface with friction slide until it starts rotating? [closed]

A bowling ball is thrown horizontally with initial velocity $v$ and no initial rotation over a surface with static coefficient of friction $\mu$. Determine the distance the ball travels ($d$) until ...
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1answer
60 views

Angular acceleration as a function of torque

I know that the angular momentum $\mathbf{L}_{cm}$ with respect to the centre of mass of a rigid body can be expressed as $I\boldsymbol{\omega}$ where $I$ is the inertia matrix and ...
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1answer
53 views

How do we “cancel out” the torque from running?

Running certainly causes a torque on our body, as we are propelled forward via our feet; why doesn't this torque cause our bodies to spin about their center of mass?
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0answers
27 views

Rotational motion of a cylinder [closed]

I was solving a problem related to rotation, and cannot get to the exact answer. The question is as follows: A cylinder of mass $m$ rests on a carriage as shown. Calculate the maximum acceleration ...
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0answers
20 views

What is happening kinematically to a car on an icy turn? [closed]

I am stumped on a conceptual homework question that involves rotational kinematics and friction. Consider a car traveling along a road that encounters a turn covered in an unseen layer of ice. ...
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0answers
31 views

Torque due to non-uniform force [closed]

Suppose a non-uniform force, varying along with the distance, is acting normally on the surface of a rod hinged at the mid point. The force varies along the length of the rod, i.e as we go down along ...
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0answers
29 views

How to calculate angular momentum in this scenario? [closed]

The answer to part a) is 1080. However, for part b) I don't understand why the equation wouldn't simply be $I_i\omega_i = I_f\omega_f$. Why do we have to subtract $m_bv cos \phi$ from ...
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1answer
39 views

How do you define the total rotational energy of an object?

This problem arose when I was applying a conservation of energy argument to a mechanics problem, (a spinning coin on a table) and wasn't sure how to define the total rotational energy of the coin. At ...
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0answers
56 views

Degeneracy of Rotational Energy Levels of a Diatomic Molecule

To derive the energy levels of a diatomic molecule (with the z axis the axis of symmetry of the molecule), we write the Hamiltonian as ...
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0answers
46 views

Rotational Spectrum of a Diatomic Molecule

The rotational energy levels of a diatomic molecule are given by $$E_l=\frac{\hbar^2}{2I}l(l+1)$$ where $l$ is an integer. If the molecule is a dipole it can emit or absorb electromagnetic radiation ...
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1answer
57 views

Rolling in V shaped groove [closed]

In this set up I've been asked to work out the linear acceleration down the slope. It's said to be instantaneously rolling around the axis AB $Ma=Mg\sin(\theta)-2F$ where $F$ is the frictional ...
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1answer
29 views

Consideration of centrifugal force during descent

If we imagine an object falling from a height h above the surface of the earth. We can go into a rotating frame and therefore introduce Coriolis and centrifugal forces. Using the Coriolis force the ...
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0answers
34 views

Name for the transformation into an accelerated frame?

A transformation into a frame that looks at an experiment from a rotated perspective is called a rotation. A transformation into a frame that moves with a different constant velocity is called a ...
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0answers
37 views

Gears in contact?

I was doing a practice exam paper question that was along the following lines: A gear, $A$,and moment of inertia $I_A$ is spinning about its axis at angular velocity $\omega$. Another gear $B$ ...
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0answers
24 views

Calculate angular velocities and alpha values?

A lightweight bar, stiff stick of length L, at either end are two small spheres of mass $m_{1} = m_{2} = m$. Bar may turn in vertical horizontal axis passing through point O on the way its a bar ...
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0answers
112 views

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
103 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
30 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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0answers
55 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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0answers
40 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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2answers
112 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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1answer
46 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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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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1answer
104 views

Coupled wheel and rod (analytical mechanics) [closed]

I am struggling with formulating the equations of motion. Consider a coordinate system with origin in $O$ ($y$ upwards and $x$ to the right), label the center of mass of rod $AB$ with $G$ then: ...
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0answers
29 views

Most general gyroscope motion [duplicate]

In Kleppner & Kolenkow's Introduction to Mechanics (Amazon link), the general gyroscope motion including nutation was derived using the approximation condition $\Omega T \ll 1$ where $\Omega$ is ...
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0answers
79 views

Rolling without slipping [closed]

A uniform, solid cylinder of mass $m$ and radius $r$ rolls without slipping down a plane, inclined at an angle $θ$ to the horizontal. You may assume, without proof, that the moment of inertia of ...
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0answers
136 views

Friction and work from torque

I would like to understand where is the error in the third case, for that I gave 2 easier cases where I'm able to find the energy from heating is equal to the energy lost by torque. Case 1/ Purple ...