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

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4
votes
3answers
210 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 ...
2
votes
2answers
84 views

Will the day/night cycle change when the poles melt?

I want to know what will happen to day and night if poles melt i think it will change but I don't know why? ^_^
1
vote
1answer
51 views

One force applied to one point of a rigid body: centre of mass and torque [duplicate]

Let us suppose that one force is applied to a point of a rigid body that is not acted upon by any other force. I think an example can approximatively be a rock in deep space, far from any relevant ...
2
votes
4answers
3k views

What is the principle behind centrifugation?

What is the principle behind centrifugation? I understand the idea that you spin something around the centripetal force will cause an apparent force on the spinning system. However I don't quite ...
3
votes
1answer
49 views

Angular momentum-torque relationship in a rotating frame?

I have read that $$\vec\tau=\frac{\mathrm{d}\vec L}{\mathrm{d}t}$$ holds true whenever the origin is not accelerating. But I cannot see why this holds true for a rotating frame of reference (such as ...
0
votes
1answer
60 views

Why doesn't the string slack in the motion in a vertical circle even if tension is zero?

Suppose a particle of mass $m$ is attached to an inextensible string of length $R$ and is undergoing vertical - circular motion. The centripetal force is given by the tension & its weight: $$T ...
0
votes
1answer
49 views

Can an object experience torque when the only applied external force is at its axis of rotation (IOW, where $F \times r = 0$)?

This question came up because of this diagram that I saw in my textbook of an angular simple harmonic oscillator. I've always struggled a bit with torque and rotational dynamics in general, and I ...
2
votes
2answers
84 views

Clarify excerpt from Feynman Lectures on rotations in three dimensions

In The Feynman Lectures, vol. I, chapter 20 Feynman discusses rotations in three dimensions and explains angular velocities may be added as vectors; in particular he says: What about angular ...
3
votes
1answer
276 views

Why are three parameters required to express rotation in 3 dimension?

We know that in spherical coordinates angle $\theta$ and $\phi$ (two angles)are enough to express three dimensional rotation of matrix. But to express rotation mathematically as a transformation ...
1
vote
1answer
53 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 ...
1
vote
0answers
52 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 ...
1
vote
0answers
42 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 ...
0
votes
1answer
112 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 ...
3
votes
1answer
2k views

Derivation of Newton-Euler equations of motion

I am in search of a simplified version of the derivation of Newton-Euler equations of motion (both translational and rotational) for a rigid body (3D block) that has a body fixed frame and where the ...
1
vote
1answer
26 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 ...
1
vote
0answers
32 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 ...
2
votes
0answers
61 views

What is the physics in a balero toy?

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 ...
0
votes
3answers
124 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 ...
0
votes
1answer
36 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 ...
0
votes
1answer
39 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 ...
3
votes
1answer
662 views

Ball Rolling Down An Inclined Plane - Where does the torque come from?

There is a ball rolling down an incline, with no slipping. If we consider the point of contact between the ball and the inclined plane to be the pivot point (for our torque calculations), then I have ...
0
votes
1answer
65 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, ...
1
vote
0answers
29 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 $B$ ...
1
vote
2answers
70 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?
2
votes
1answer
66 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 ...
0
votes
2answers
32 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 ...
1
vote
4answers
285 views

Why is moment of inertia dependent on $r^2$ and not on $r$ ? (physical reason)

Moment of inertia is the mass equivalent in rotational dynamics. I know , by mathematical arguments, moment of inertia of a particle is $$ I = \text{mass} \cdot r^2$$ . But what is the physical ...
1
vote
1answer
57 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 ...
-1
votes
1answer
59 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
0
votes
1answer
53 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 ...
1
vote
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?
1
vote
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 ...
1
vote
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 ...
0
votes
3answers
73 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 ...
4
votes
1answer
110 views

In 2-dimensional and 3-dimensional universes, stellar systems and galaxies are flat and disky. But what about in 4-dimensional universes?

I just watched that interesting video: https://www.youtube.com/watch?v=tmNXKqeUtJM In 2 dimensions a cloud of particles rotating in a plane is flat by definition since it's in 2 dimensions. ...
3
votes
5answers
271 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, ...
0
votes
2answers
100 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
131 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
82 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
136 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
7k 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
80 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
49 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
159 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
59 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
82 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
109 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
vote
0answers
84 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
80 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 ...