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

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0
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2answers
126 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. ...
-1
votes
3answers
158 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) ...
1
vote
1answer
92 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: ...
4
votes
2answers
142 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 ...
21
votes
7answers
8k views

Why don't spinning tops fall over?

One topic which was covered in university, but which I never understood, is how a spinning top "magically" resists the force of gravity. The conservation of energy explanations make sense, but I don't ...
2
votes
1answer
82 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 ...
0
votes
1answer
81 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.
2
votes
1answer
190 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 ...
0
votes
1answer
70 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 ...
0
votes
1answer
87 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 ...
0
votes
2answers
125 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. ...
1
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0answers
130 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 ...
0
votes
1answer
102 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?
32
votes
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 ...
1
vote
1answer
106 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 ...
1
vote
1answer
32 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 ...
2
votes
1answer
203 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 ...
1
vote
2answers
59 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 ...
0
votes
2answers
638 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 of ...
13
votes
10answers
19k views

What do people actually mean by “rolling without slipping”?

I have never understood what's the meaning of the sentence "rolling without slipping". Let me explain. I'll give an example. Yesterday my mechanics professor introduced some concepts of rotational ...
0
votes
2answers
113 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 ...
21
votes
4answers
9k views

Stability of rotation of a rectangular prism

I've noticed something curious about the rotation of a rectangular prism. If I take a box with height $\neq$ width $\neq$ depth and flip it into the air around different axes of rotation, some motions ...
1
vote
1answer
67 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 ...
0
votes
0answers
31 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
vote
1answer
88 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
vote
2answers
64 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} ...
1
vote
1answer
98 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 ${\bf{J}} _{\Omega}$? ...
-1
votes
1answer
55 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?
2
votes
0answers
81 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 ...
2
votes
3answers
91 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.
2
votes
2answers
305 views

Approximating Rolling/Sliding in 2D Shape

I'm trying to find more information on how a 2D shape (could be defined by a function, such as ellipse, or by a polygon) will roll across a surface. The shape could be nearly circular or quite ...
1
vote
2answers
130 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 ...
0
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0answers
30 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 ...
0
votes
1answer
64 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 $\mathbf F$ ...
1
vote
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 ...
0
votes
1answer
79 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 ...
37
votes
7answers
4k views

Why does everything spin?

The origin of spin is some what a puzzle to me, everything spin from galaxies to planets to weather to electrons. Where has all the angular momentum come from? Why is it so natural? I was also ...
13
votes
3answers
1k views

What is the physics of a spinning coin?

When we spin a coin on a table, we observe 2 things: It slows down and stops after sometime. It does not stay at just one point on the table but its point of contact with table changes with time. ...
5
votes
2answers
232 views

How to model energy loss in a rotating body?

I recently asked a question about modeling instability in a rotating rigid body. I now realize that I was mentally confounding two different effects: The "Dzhanibekov effect" in which a rigid ...
2
votes
3answers
67 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 ...
1
vote
0answers
43 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) ...
2
votes
0answers
69 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 ...
0
votes
0answers
59 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 ...
0
votes
1answer
34 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. ...
1
vote
2answers
118 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 ...
0
votes
2answers
53 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 ...
0
votes
0answers
90 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 ...
0
votes
1answer
52 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
votes
2answers
194 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 ...
0
votes
3answers
90 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 ...