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

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3answers
281 views

Mass equals Moment of inertia when constant density?

I have found equation for moment of inertia $(J)$. I'm calculating $J$ for hemisphere, with rotational axis $Z$. $$ J = \iiint\limits_V r^2 \cdot \rho \cdot dV $$ But if $\rho$ is constant ...
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1answer
23 views

Rotational dynamics about a point or an axis?

In several books and sites, its written that torque is calculated about an axis and angular momentum is calculated about a point. In MIT's Angular momentum lecture pdf, Angular momentum has been ...
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2answers
32 views

Rigid bar on the floor of a rotating space station

I read this in a comment to an answer in physics.stackexchange.com. The comment was An easier method might be to just place a straight, rigid beam on the floor. If you find the floor is concave, ...
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1answer
189 views

Can a ball stay still while laying on a inclined plane?

Suppose there is a ball on an inclined plane. So, there are three forces acting on it: normal force from the plane, gravity (which can be decomposed in the component of gravity perpendicular to the ...
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1answer
298 views

Model the gyroscopic effect for 3axes stabilisation

Context I am trying to stabilise a platform on a guimbal using 3 axes gyroscopes. I have made tons of research (same problem for weeks even months now) without being able to properly model the 3 ...
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1answer
68 views

Will it start rolling?

Suppose you have a wheel standing stationary on a rough horizontal surface. Now you apply a horizontal force at the top of the wheel. Now, will the wheel experience any force or will it just start ...
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1answer
53 views

If the axis of rotation is fixed, is it ok to say clockwise torque?

I know that the direction of torque is along the axis of rotation, but would it be acceptable to say, for example considering a vertical thin rod in the x-y plane with a force acting on the bottom end ...
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2answers
158 views

Inertia matrix of a rod rotating about an axis [closed]

I'll provide a picture for clearer understanding. The problem is to calculate the angular momentum of the rod rotating about the z-axis. I have serious difficulties in deriving the inertia matrix, ...
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1answer
56 views

Finding acceleration using rotational dynamics [closed]

I'm asked to find the linear acceleration of this object for a given tension $T$ knowing that both discs have mass $M$ and we don't consider the mass of the bar. The answer of the book is ...
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1answer
141 views

Purely mechanical description of how gravity causes a gyroscope to precess

I know the vector equation that relates torque to moment of inertia and angular momentum. What I want to know is what physical mechanisms actually occur to keep the gyroscope from falling. Where is ...
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1answer
219 views

Contradiction regarding friction of a rolling cylinder in an inclined plane

I came upon this while wondering whether the friction of a rolling cylinder on an inclined plane depends on the value of friction coefficient. now, $$f\leqq\upsilon N$$ Again after calculating I ...
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1answer
254 views

Centrifugal force acting on ring [closed]

Take for example the case of a rod rotating about an axis passing through its centre of mass and perpendicular to it. It has a ring hung from one of its sides. The rotation of the rod causes the ring ...
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1answer
374 views

Will a free-falling rod (without drag) rotate?

When we consider a bicycle is turning on a flat plane, we know that there is friction, which provide centripetal force on the bicycle. And we know that the bicycle is no longer perpendicular to the ...
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1answer
75 views

Why do cosmic bodies revolve? [duplicate]

Why do cosmic bodies such as planets, stars, satellites revolve? What made them to revolve after the formation of universe?
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2answers
4k views

DC Motor Torque Constant

I am very new to DC motors and to stackexchange. Please correct me if anything I said does not make sense. For DC motors, the equation looks like this: $P = \tau\dot{\theta}$ where $P$ is power, ...
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1answer
996 views

Finding Rotational Kinetic Energy Of A Clock

The problem I am working on is: Big Ben, the Parliament tower clock in London, has an hour hand 2.70 m long with a mass of 300 kg, and a minute hand 4.20 m long with a mass of 100 kg (see figure ...
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2answers
5k views

Tensions And Pulleys With Masses

The problem I am working on is: "A block of mass m1 = 1.80 kg and a block of mass m2 = 6.30 kg are connected by a massless string over a pulley in the shape of a solid disk having radius R = 0.250 m ...
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2answers
613 views

Setting up equations for a Rotational Kinematics system

I'm having a hard time setting up equations for the following problem: A green hoop with mass $m_h$ and radius $r_h$ m hangs from a string that goes over a blue solid disk pulley with mass $m_d$ ...
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3answers
10k views

Finding Angular Acceleration of rod given radius and angle

A uniform rod is 2.0 m long. The rod is pivoted about a horizontal, frictionless pin through one end. The rod is released from rest at an angle of 30° above the horizontal. What is the angular ...
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2answers
513 views

Precession of angular velocity about the body-fixed axis

My textbook mentions that under force-free motion of a symmetric top, its angular velocity vector $\overrightarrow \omega$ precesses about the $z$-axis of the body-fixed coordinate system. This seems ...
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1answer
115 views

Period of an Object in Periodic Motion

My attempt (if it matters): The initial period is given by $T_X = \frac{2\pi X}{v}$ for some $v$. The new period is given by $T_Y = \frac{2\pi Y}{v}$ for the same $v$. $Y = \frac{X}{2}$, so ...
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2answers
5k views

Rotational kinetic energy during vertical circular motion of a particle

Why is it not necessary to take into account rotational kinetic energy when using the Law of Conservation of Mechanical Energy to solve vertical circular motion problems? After all, the particle is ...
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1answer
246 views

Relationship between the “angle of the floor” and the angular velocity in a banked turn?

Wel, imagine that you're in a carousel, and the floor is, let's say at $\theta=0$ so it's totally horizontal, if $\theta=90$ the floor would be vertically. The object put above the floordoesn't move ...
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1answer
349 views

Angular velocity $\omega$ by $v$

We have two girls, with mass ($M$). They become close to each other in speed of $V$. The distance between them is $3L$. I was asked to calculate the Angular velocity ($\omega$) of the two girls. So ...
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1answer
239 views

What causes a gyroscope to eventually rotate/fall over?

Hey so I've just learned about angular velocity and momentum and how torque changes it. Looking at a wheel spinning around an axis, with one end being held up by a rope, what causes the wheel to ...
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1answer
19 views

When conserving angular momentum, about which point(s) should it be calculated?

In my physics problem I have a ball fired at a non fixed bar, which is moving at some velocity, causing them both to stick together and the bar-ball pair to rotate about the new center of mass. About ...
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1answer
24 views

What forces cause the centripetal acceleration in circular motion on a merry-go-round?

Suppose you stand on a merry-go-round spinning at $f$ revolutions per second and you are $R$ meters from the center. What forces act on you? If you were tied to a rope like in Fig 2 you would follow ...
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1answer
84 views

The direction of frictional force in smooth rolling motion

I want to ask about the direction of frictional force in smooth rolling motion which means the rolling object doesn't slide on the surface. Here is the first case, the wheel rolls to the right so the ...
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1answer
29 views

$y$-component of center of a cube that rolls without slipping [closed]

For the figure above, let $O$ be the origin point for $x,y$-axis, and $+x$ goes to the horizontal right direction while $+y$ direction goes to the up direction. The figure has one circle and one ...
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1answer
71 views

Rotational Inertia of Two rods [closed]

In the figure, two particles, each with mass $ = 0.82 \text { kg}$ are fastened to each other, and to a rotation axis at $O$, by two thin rods, each with length $d = 5.3 \text { cm}$ and mass $M = 1.0 ...
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2answers
59 views

Angular momentum in rotational motion

Ok so there are two things that have completely confused me- things related tangular momentum. 1.)First of all, how can a body possess angular momentum even though it is not rotating. according to ...
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2answers
47 views

Cylinder falling down the edge of a table [closed]

Suppose, a cylinder is placed on its lateral side at the edge of a table, carefully, so that the slightest push makes it fall from the table. We give it a gentle push. And it begins to fall. How is ...
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1answer
48 views

Is a motor HP torque directly proportional to the increasing HP among identical motors?

Say you have three motors: Motor 1 = .10 HP with x torque, performing task A Motor 2 = 1 HP with y torque, performing task A Motor 3 = 10 HP with z torque, performing task A If the motors are the ...
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1answer
57 views

Why is the slippage constraint for one moving cylinder and one fixed cylinder $r(\phi - \theta)=R \theta$? [closed]

Why is the slippage constraint for one moving cylinder and one fixed cylinder $r(\phi - \theta)=R \theta$? Every time I write it down on paper I get the result $r\phi = R \theta$. I am not sure if I ...
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1answer
83 views

Feynman's explanation of parallel axis theorem

In the book Feynman's Lectures on physics volume 1 chapter 19, He explains prallel axis theorem as follows. Suppose we have an object, and we want to find its moment of inertia around some ...
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1answer
23 views

Angular momentum of a sphere moving vertically downwards [closed]

If a solid sphere is moving vertically down with a velocity $v$ and spinning with an angular velocity $\omega$, what is the angular momentum of the sphere about an axis through the sphere which is at ...
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1answer
159 views

Small sphere rolling off the top of a large sphere [closed]

A heavy sphere of radius r = 1.00 meter is fixed with respect to the ground. A small uniform solid sphere is placed at the top of the larger sphere. After a slight disturbance, the smaller sphere ...
0
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1answer
283 views

Moment of inertia of a cylinder about its base

I've tried to find the moment of inertia of a cylinder rotating about an axis parallel to its base (i.e about the 'End diameter') as one can see here . But when I checked my results with different ...
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1answer
65 views

How can a generalised force be dependent on an angle i.e. not a vector?

I'm currently working through an example question in Patrick Hamill's 'A Student's Guide to Hamiltonians and Lagrangians'. The question I'm having conceptual difficulty with is: A particle is ...
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1answer
195 views

Does a rotating plank only acquire rotational kinetic energy?

I have another doubt with a Kleppner problem :(. A thin plank of mass M and length l is pivoted at one end. The plank is released at 60$^{\circ}$ from the vertical. What is the magnitude and ...
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1answer
94 views

Does a spinning part affect the moment of inertia of a composite object?

I have been going back through some Kleppner problems and have a doubt concerning problem 6.18. It states: Find the period of a pendulum consisting of a disk of mass $M$ and radius $R$ fixed to ...
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2answers
102 views

Rotational behavior of objects in zero-g with forces [closed]

I would like to know how this object would rotate in free space out of curiosity. Below is a diagram of the object. It is of uniform density and has a center of mass in the center of the object, ...
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1answer
76 views

Finding the minimum radius of the pivoted disc

Here is a question based on Simple Harmonic Motion that I tackled just now. However I think I am having an approach to tackle this but I am not sure about it. Ouestion: A uniform disc of radius ...
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1answer
47 views

Calculating the components of angular momentum of a rigid body

You have a rigid body with 1 fixed point in space (the origin). It's self-explanatory how to get the following equation for the angular momentum: $\vec L = \sum_n m_n\vec r_n\times\vec v_n$ ...
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1answer
57 views

Moment of inertia of a hollow sphere wrt the centre?

I've been trying to compute the moment of inertia of a uniform hollow sphere (thin walled) wrt the centre, but I'm not quite sure what was wrong with my initial attempt (I've come to the correct ...
0
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1answer
40 views

Rotating frames [closed]

A bird of mass $m$ is on a merry-go-round of radius $a$ which rotates at constant angular velocity $-\omega_b$ in the $y$ direction. A woman of mass $M$ is on a second merry-go-around of radius $b$ ...
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1answer
203 views

Torque and angular acceleration with bicycle wheel

This might be a simple problem for many of you. However, please help me understand it too. I have been looking trough a lot of materials online, and I still have the following questions, that would ...
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2answers
428 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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3answers
116 views

Rotating reference frames

I'm trying to understand the equations that govern velocity in a rotating reference frame... \begin{equation} v_i = (\frac{dr}{dt})_r + \Omega \times r . \end{equation} I'd like to build a simple ...
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1answer
2k views

How do I calculate the experimental and theoretical rotational inertia of a point mass?

I'm getting some weird results from a calculation I'm doing and quite honestly, I'm pretty sure it's my fault. I do have an apparatus involved for the experimental process for my lab but I don't think ...