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

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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
233 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 force ...
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1answer
37 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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3answers
886 views

How can I relate linear and angular motion using a single formula?

I want to relate linear and angular motion using a single formula. Assume I have a 10m rod, and I apply a force of 5N on it, 2.5m away from the axis of rotation for 1s. How can I determine the ...
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45 views

A free axis of rotation [duplicate]

It is claimed that the free axes of rotation of a rigid body are the ones with the smallest and the largest moment of inertia. Why? How can we determine which free axis of rotation will be used?
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45 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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1answer
223 views

What is the physics in a balero toy? [closed]

A balero is a wooden ball tied with a string to a rod. The string ties to the ball at one end (say North pole), and there is a hole drilled in the ball at the other end (South pole). The hole is the ...
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1answer
104 views

Angular velocity formula for a particle?

I know that when the motion of a particle is circular about the origin then: $$\vec v=\vec \omega \times \vec r$$ But that this does not hold for any motion with a radial as well as tangential ...
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3answers
416 views

Torque on a disc?

In the following diagram: Point(c) is a going into the page and attached to the disc, Point(c) applies a torque($\tau$) to the disc, and it starts to rotate due to that torque. And if point(c) was ...
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1answer
134 views

Cancelling internal forces/moments term when deriving inertial matrix

I am attempting to derive the inertial matrix for a general rigid body of mass $m$ as shown in the following diagram: The green vectors indicate the key position vectors: Position of centroid ...
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1answer
250 views

Since Earth spins, would an aircraft travelling opposite to direction of Earth spin take less time? [duplicate]

Suppose we want to reach the point on earth which in relative terms is exactly on the opposite end of the sphere we call earth (I know it is not an exact sphere). We either dig vertically downwards, ...
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0answers
149 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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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
334 views

Ball rolling on half-pipe

It is well-known that a ball rolling down a half-pipe where the side it starts on has enough friction for the ball to roll without slipping and on the side other to be frictionless, that the ball will ...
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1answer
801 views

Finding time period of oscillations in a multiple spring system attached to a solid cylinder [closed]

A solid cylinder of mass $m$ and radius $R$ is kept in equilibrium on horizontal rough surface. Three unstretched springs of spring constant $k$, $2k$, $3k$ are attached to cylinder as shown in the ...
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2answers
46 views

When I change the rpm of a turntable, how long does the turntable to get to the new rpm?

If the turntable was rotating at 16 rpm and I switched it to 30 rpm, is the change in speed pretty much instantaneous, or is their a period of acceleration? When I did it, the change appeared to be ...
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1answer
116 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
150 views

A Textbook Problem From Rigid Body Dynamics(Cengage Bm Sharma) [closed]

I was going through my textbook examples on rigid body motion. In this problem i can understand the derivation of equations 1,2 and 3,but can someone explain me the 4th equation?Please!!1
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1answer
216 views

Rotational Equilibrium Problem [closed]

The question is as follows: One end of a uniform 4.0-m rod, whose weight is w, is supported by a cable that makes an angle of 37° with the horizontal. The other end of the bar rests against a wall ...
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2answers
286 views

Reaction to gyroscopic force [duplicate]

Just like the reaction of the weight of a body is a force acting on Earth towards the body, where and in what direction does the reaction of a gyroscopic force act?
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3answers
207 views

Maximum acceleration for a vehicle [closed]

I'm in engineering school and we have a project: we have to build a amphibioues vehicle; I'm looking for a formula. Our vehicle has to go as far as possible with its unique source of energy, a ...
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3answers
729 views

Finding the angular velocity of a rod hit at a distance from its pivot [closed]

A 1m long, 2kg stick is nailed to the wall with a single nail, allowing it to pivot and freely rotate at the end. A 1kg ball, with speed 3m/s makes contact with the stick at some distance x (unknown) ...
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1answer
867 views

If I bend a rod, will its moment of inertia change?

In the first picture, there is a homogeneous metal rod of length $2L$ and mass $M$. If it rotates around a normal axis passing by $O$ (which is the center of gravity), then its moment of inertia is: $...
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2answers
2k views

How to determinate the minimum period of oscillation for a physical pendulum? [closed]

A physical pendulum consists of a thin homogeneous rod of length $l$, suspended by a point $O$ at a distance $x$ from the center of gravity ($x<\frac{l}{2}$), oscillating in a vertical plane. For ...
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5answers
727 views

How is Angular Momentum Conserved when Mass is Released?

I am not a physicist (math/comp-sci) but I understand that Angular Momentum is supposed to be conserved. I find this confusing because there seems to be many simple, common cases where a restrained, ...
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2answers
151 views

Can net torque $\sum_i\mathbf r_i\times\mathbf F_i$ be expessed as $\mathbf r\times$ (net force) for some $\mathbf r$?

Let $\mathbf F_i$ be forces each of which is applied on $\mathbf r_i$ of a rigid body. Then is there a position vector $\mathbf r$ that satisfies $$\displaystyle\sum_i\mathbf r_i\times\mathbf ...
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1answer
214 views

How much energy would it take to stop Earth's rotation on its axis?

I see a lot of questions regarding situations what would happen if the world would stop spinning. This got me to wondering how much energy it would actually take to stop the world from spinning.
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1answer
695 views

During a turn, do the rear wheels necessarily trace out the same arcs as the front wheels?

When a vehicle makes a turn, the two front wheels trace out two arcs as shown in the figure below. The wheel facing towards the inside of the turn has a steering angle that is greater than that of the ...
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1answer
121 views

A problem about harmonic oscillators

A ball with mass $m$ and radius $r$ rolls without sliding inside a cylinder with radius $R (R>>r)$, with $\theta <<1$. Find the angular frequency $\omega$ What I Know: There are ...
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1answer
111 views

How to calculate the energy required to rotate a planet?

How to calculate the energy required to rotate a planet from non-rotating state? Say the planet is Venus with equally distributed mass of $4.8676 \times 10^{24}$ kg, and desired rate of 1 rotation per ...
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2answers
179 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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320 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 \end{...
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1answer
397 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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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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1answer
176 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
718 views

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

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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2answers
76 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
216 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 ...
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2answers
1k views

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

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 ...
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1answer
93 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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1answer
129 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 ...
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2answers
76 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} \frac{\pi}{2}\...
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2answers
181 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
195 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
131 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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180 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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1answer
157 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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57 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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2answers
152 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
125 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 ...