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

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2
votes
0answers
69 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
135 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
47 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
45 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
752 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
87 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
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 $B$ ...
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
78 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
35 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
307 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
65 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 ...
-2
votes
1answer
61 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
62 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
80 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
112 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
299 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
111 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
146 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
86 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
140 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
81 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
58 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
173 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
66 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
121 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
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 ...
0
votes
1answer
90 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
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 ...
1
vote
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 ...
2
votes
1answer
181 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
52 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
614 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
18k 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
99 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
64 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
87 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
62 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
94 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
53 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
80 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
86 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.