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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1answer
26 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 ...
1
vote
1answer
53 views

Rotation and fictitious forces

A bug eats through an apple and forms a vertical, infinitesimally thin canal parallel to the vertical diameter at a distance $\frac{R}{2}$ from the center. The apple rotates at angular velocity around ...
0
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1answer
30 views

Rotating frames [on hold]

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 $b$ ...
2
votes
1answer
97 views

Sum of forces with liquid in rotation

It's not homework (I'm teacher). I would like to compute sum of forces on this study : The shape is symmetrical like that I'm sure the center of gravity is in the center of the shape. I compute ...
0
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1answer
59 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 ...
3
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2answers
53 views

What is an intuitive explanation using forces for the equatorial bulge?

The earth is not a sphere, because it bulges at the equator. I tried fiddling with centripetal force equations and gravity, but I couldn't derive why this bulge occurs. Is there (a) a ...
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1answer
46 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
64 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, ...
0
votes
1answer
26 views

Coordinate System vs. Angular Properties vs. Centroid

Please help me check my understanding related to the rotational motion of a 3D rigid body after reading some Physics textbooks and googling for some more materials (e.g., Wikipedia's Torque, ...
1
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1answer
31 views

Moment of inertia of a sphere

I'm looking at sample calculations of moment of inertia of a sphere here. In the first example (disc method), it has the integral as $dI = \frac{1}{2}r^2 \,dm$, while in the second example (shell ...
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0answers
34 views

Why does pitch in a helicopter take effect 90 degrees later?

In a helicopter if you want to give it a forward pitch, you change the angle of the blades when it is in this position ---- So the two blades experience unequal lift and because o gyroscopic ...
1
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0answers
60 views

Restrained double pendulum

The equations of motion of a double pendulum are well-known. Usually you'd have the them expressed in the rotations $\theta_1(t)$ and $\theta_2(t)$. There are two degrees of freedom. Now consider the ...
2
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2answers
41 views

Describing a motion of gyroscope with gimbal

Can you tell be how to set the equations to describe the motion of this machine in movie "Contact": https://www.youtube.com/watch?v=TSaO9VGjLXc This is gyroscope with gimbal, am I right?
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0answers
45 views

How much energy would you need to halt Earth's spin?

I was curious about the feasibility of stopping the Earth from spinning. A way to start I suppose is by getting an idea of the theoretical energy requirements.
0
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1answer
34 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 ...
0
votes
2answers
98 views

Is it possible to calculate how fast something will roll down a hill?

If I have a wheel, I know it's mass and diameter and the slope of a hill. Can I calculate the time it will take to get to the bottom of the hill? I am doing a project for my science fair and I sent 5 ...
1
vote
2answers
67 views

Rod sliding on a frictionless surface

A uniform rod$(m,l)$ is standing vertically on a horizontal frictionless surface. Gravity is downwards and uniform. I give its upper end a little push and off it goes. I want to find the Normal ...
1
vote
1answer
67 views

Calculating the time to stop a wheel with friction [closed]

I'm trying to solve the following problem, but i have no idea how to begin. A wheel of mass $M$, radius of gyration $k$, spins smoothly on a fixed horizontal axle of radius a which passes through ...
1
vote
2answers
20 views

Rotational Velocity and Rotational Frequency

What is the difference between rotational velocity & rotational frequency? Their units seem to be the same, and I've read that one is a 'scalar' and the other is a 'vector,' but how do they ...
0
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0answers
23 views

An easy source to understand classical dynamics — Rigid body Rotation [duplicate]

I've been having an extremely hard time at understanding rigid body rotation. The source that I'm currently studying from has been suggested by 't Hooft on his webpage. It's by Richard Fitzpatrick. ...
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2answers
49 views

Eulerian Angles — Why three rotations can transform fixed frame into body frame?

"In general, if we restrict ourselves to rotations about one of the Cartesian axes, three successive rotations are required to transform the fixed frame into the body frame" The origin of our fixed ...
1
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0answers
56 views

Having trouble with a homework problem involving rotation [closed]

This is for a past homework assignment so it's already been solved. We wrap a light, nonstretching cable around a 9.00kg solid cylinder with diameter of 34.0cm . The cylinder rotates with ...
0
votes
1answer
82 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'}, ...
1
vote
1answer
63 views

A question about biceps and rotational equilibrium

I know that as the angle of the elbow increases, the force of the bicep increases. i.e. when angle is 180, arm is fully extended and there is 0 force from bicep. When the elbow angle is smaller there ...
0
votes
1answer
54 views

When does the angular momentum point in a different direction from the angular velocity?

I read this somewhere: $$\mathbf{L} = \tilde{\mathbf{I}}\mathbf{\omega}$$ In general, the angular momentum vector, $\mathbf{L}$, obtained from Equation above, points in a different direction to the ...
-1
votes
1answer
41 views

Linear speed of falling pencil [closed]

Find the final linear speed of pencil. Pencil would move because of gravity. Let's assume that it is balancing on the tip. We do not take friction into consideration. – Given $$d=0.15m$$ Similar ...
0
votes
3answers
85 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 ...
4
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0answers
67 views

What makes a wrist-energized gyroscope rotate faster?

I'm considering a wrist-energized gyroscope, shown below (after my daughter let it fall and it broke open). That one was sold as Roller Ball, but variants are known as Powerball, DynaBee, Dynaball, ...
0
votes
1answer
33 views

Thrust to Weight ratio in Space with an off set CoM

With regards to this thread, Thrust center in space My question is, if the thrust to weight ratio was increased so that it was much higher than the weighted mass of the sphere (ship), would the ...
0
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0answers
64 views

Imagine a 50-mile tower spanning from desert floor to the Karman Line

CORRECTION: The structure weighs 1.568E15 kg.s Does the structure effect the equilibrium of earth's rotation? Would momentum from Earth's rotation apply lateral force to the structure? What else do ...
0
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0answers
19 views

model for flexible stick

I'm trying to model a flexible stick with a partial differential equation. I want one of the ends to be fixed and the other end to swing. Do you guys know of any good models I can use? Any ...
1
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2answers
67 views

Direction of friction for object that rolls with slipping

Let's say you hit a cue ball with a pool stick that causes an impulse. If the pool stick hits the ball above the ball's center of mass, is the direction of friction different than if the pool stick ...
2
votes
1answer
61 views

Find Angular Momentum about any point

How do I find the angular momentum of a body about any point? We know that $L=I\omega$ for a body rotating in space, where $L$ denotes the angular momentum, $I$ denotes the moment of inertia and ...
0
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1answer
66 views

Why is it easier to turn a heavy hanging object?

Assume if we had a 2 tonne weight placed on ground attached with a rope that we can use to turn the object around. It will immensely hard to turn that object around by pulling the rope. However, if ...
2
votes
1answer
97 views

Lagrangian approach to spinning thread reel

I am trying to better understand Lagrangian dynamics and am struggling to complete the following question: A reel of thread of mass $m$ and radius $r$ is allowed to unwind under gravity, the upper ...
0
votes
1answer
43 views

Force on a line

Say you have a rigid line of mass $m$ and length $\ell$ along the $x$ axis and you apply a constant force $f$ at one end in a direction that is always perpendicular to the line, starting in the $y$ ...
-1
votes
2answers
76 views

Circular motion, deciding what the tangential speed must be to maintain theta [closed]

A bob of mass m = 0.250kg is suspended from a fixed point with a massless string of length L = 25.0cm . You will investigate the motion in which the string traces a conical surface with half-angle θ = ...
3
votes
2answers
47 views

Taking pivot about an accelerating point

Given this question: A small ball of mass $m$ and radius $r$ rolls without slipping on the inside surface of a fixed hemispherical bowl of radius $R>r$. What is the frequency of small ...
2
votes
0answers
66 views

Understanding gyroscopes

Considering the typical situation of a rotating bicycle wheel held by one end of its axle by a rope tied to the ceiling: gravity torque is the time derivative of the angular momentum, and in this case ...
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0answers
43 views

Rotation motion like the number 8

I'm a college student majoring in culinology and I'm trying to find out the reason or method of the number 8 motion. Responses doesn't have to be in culinology examples, but that would be a great help ...
2
votes
1answer
79 views

Maximum permissible speed while going down a ramp

So, I was playing hill climb racing and I noticed that if we move with high speeds towards a ramp going down we just jump it off. While lower speeds, help us to stay in contact with the ramp. ...
2
votes
0answers
46 views

Why does the video recorded by a falling, rotating camera seem to stabilize?

Here is a video of a GoPro falling from a plane: http://www.youtube.com/watch?v=QrxPuk0JefA Any idea what is happening when the image "stabilizes" around 0:35? I think it is because the camera's ...
0
votes
0answers
189 views

Different directions of frictional force when objects are rolling

My textbook has two instances of rolling bodies (smooth rolling). In the first, the body is rolling on the horizontal floor with some acceleration of its centre of mass. In this case, the book says ...
0
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0answers
28 views

Quantify the “stiffness” of a 3 axes gyroscope

Imagine a platform on a spherical joint/guimbal at its centre. The platform has 3 reaction wheels that act as a 3 axes gyroscope by rotating at a middle setpoint. The system {platform;wheels} has its ...
3
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2answers
66 views

Top angular speed of electric motor

I recently came across a question asking the following: If a motor is switched on, it quickly reaches a top speed. Why does it not just go faster and faster and faster? I thought it might be ...
0
votes
1answer
38 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 ...
4
votes
2answers
172 views

Angular momentum in a rod rotating around one end?

Sorry if I can't get straight to the point, I have to give a lot of details before I actually state the question. The formula for angular momentum is $L=I \omega$. If we look up $I$ for a thin rod ...
0
votes
1answer
75 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 ...
2
votes
0answers
70 views

Push a box in a plane with friction. How to deal with the rotation?

Suppose I have a box (say, length-1m, width-1m, height-0.5m) on the plane with friction. I can apply a horizontal force in on the surface of the box. If the force doesn't pass through the center of ...
2
votes
1answer
102 views

Velocity of hitting the ground when falling forward

A friend of mine fell while he was snowboarding which led to a discussion. He mentioned that, in general, if your center of mass is traveling at a certain velocity, and you fall forward, your head ...