A tag for questions about the mechanical interactions of rotating objects, including torque and angular momentum.
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2answers
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Deriving $T = F\ r = I\alpha$ for a rigid body
For a single point mass :
$\tau=F_{t}r=ma_tr=(m r^2)\alpha = I\alpha$
For multiple point masses bound together : $\sum \tau_i = (m_ir_i^2)\alpha = I\alpha$
But how do we go from that to $I\alpha = ...
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1answer
33 views
Intuitive explanation for why same force applied farther from a hinge causes larger angular acceleration than if applied closer?
A standard example of a problem involving torque is opening a door - the same force F applied far from the hinge causes a larger angular acceleration than if applied close to the hinge.
I always had ...
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1answer
26 views
A rod of length $L$ & mass $M$ is rotating in a circle about one end then calculate tension in the rod at a distance $x$ from the support
A rod of length L & mass M is rotating in a circle about one end then calculate tension in the rod at a distance 'x' from the support ?
For its solution why should we take mass of L-x portion of ...
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1answer
56 views
Physics of the point of contact for a spinning top
I understand how spinning tops don't tip over, cf. e.g. this and this Phys.SE questions. What I'm more interested is in identifying the factors that determine the direction the spinning top moves to?
...
4
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5answers
142 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 ...
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1answer
85 views
How is torque equal to moment of inertia times angular acceleration divided by g?
How is the following relation true
$$\tau = \large\frac{I}{g} \times \alpha$$
where $\tau$ is torque,
$I$ is moment of inertia,
$g= 9.8ms^{-2}$,
and $\alpha=$ angular acceleration.
2
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1answer
113 views
Angular momentum conservation while internal frictional torque is present
So this appears in a problem which looks simple enough in its context; It's something like this:
Two discs, A and B, are mounted coaxially on a vertical axle. The discs have moments of inertia $I$ ...
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1answer
44 views
Calculating the moment inertia for a circle with a point mass on its perimeter
I want to calculate the tensor of the moment of inertia. Consider this situation:
The dot represents a points mass, in size equal to $\frac{5}{4}m$. $m$ is the mass of the homogenous circle. I'm ...
0
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1answer
49 views
Finding the moment of inertia through superposition?
Let's say I have a body consisting of two homogenous spheres/balls that touch each other. I also have a body fixed coordinate system which consists of that body's principal axes. I know the the moment ...
6
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0answers
113 views
What determines the angle of the cushion on a pool table?
If you look at the cushions (bumpers) on a pool table, you'll see that they're not vertical. They're tilted inwards. About 10 years ago, I came across a physics exam in which one of the problems ...
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1answer
79 views
Double Compound Pendulum: why use inertia about the center of mass for bottom pendulum?
I'm trying to wrap my head around the kinetic energy of a double compound pendulum, like the one shown in the Wikipedia article on double pendulums.
I know for computing the kinetic energy of the ...
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1answer
41 views
Rotational Dynamics
In studying rotational dynamics of a rigid body , I can't seem to understand why you can solve the problem correctly only using certain points in a body and not all ? Means angular momentum and torque ...
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1answer
94 views
Confusions about rotational dynamics and centripetal force
I am a high school student. I am having confusions about the centripetal force and rotational motion . I have known that a body will be in rest or in uniform velocity if any force is not applied. But ...
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1answer
35 views
Rotational Kinetic Energy of a rigid root - Full workings Provided?
Part v is where I'm stuck.
Here is the question with my workings
If I can find Torque I can find L and using the equation $L=Iw$ I can find the w value and hence using $w=2pi*f$ I can prove it ...
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0answers
84 views
Equivalence between a charged rotating cylinder and a solenoid
Suppose we have a cylindrical shell of radius $r$ with surface charge density $\sigma$. Then we start rotating the cylinder at an angular speed $\Omega$. You can show that in this case the surface ...
2
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3answers
147 views
Newton's Second Law Equivalent in rotational dynamics
The law that
$$\frac{d\vec{L}}{dt}= \vec{T}$$
where $\vec{T}$ is torque about a frame's origin $o$ and $\vec{L}$ is the angular momentum about that origin $o$.
Can this law be ultimately (always?) ...
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0answers
35 views
Mechanics: collision & rotation [closed]
A rod AB of mass M and length L is lying on a horizontal friction less surface. A particle of mass m traveling along the surface hits end A of the rod with a velocity 'v' in a direction perpendicular ...
0
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3answers
73 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 ...
0
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2answers
70 views
What's the motion of this yoyo under external force will be?
A yoyo on a horizontal table is being pulled by a string to the right, the table is not frictionless. If we only know that the object doesn't slip, how do we know if the string is winding up or ...
1
vote
1answer
95 views
Moment of inertia of a yo-yo
Considering the yo-yo like two CDs with a hollow cylinder between them, what is the moment of inertia of that object?
The axis that I must choose can't pass through the CM and be parallel to ...
3
votes
2answers
137 views
what's the physical significance of the off-diagonal element in the matrix of moment of inertia
In classical mechanics about rotation of rigid object, the general problem is to study the rotation on a given axis so we need to figure out the moment of inertia around some axes. In 3-dimensional ...
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1answer
144 views
Cylinder rolling down an inclined plane held by a string
A cylinder of mass M and radius R is in static equilibrium as shown in the diagram. The cylinder
rests on an inclined plane making an angle with the horizontal and is held by a horizontal string
...
0
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2answers
117 views
Rolling ball which slips
A bowling ball of mass $M$ and radius $r_0$ is thrown along a level surface so that initially ($t = 0$) it slides with a linear speed $v_0$ but does not rotate. As it slides, it begins to spin, and ...
2
votes
1answer
101 views
Optimal door opening
This is a problem that has been periodically bugging me, so I finally decided to work on it. I haven't done any physics since high school, so I'm a bit out of practice:
Consider a doorway with two ...
4
votes
4answers
140 views
Wheel locks and spinout
Imagine driving in a straight line on a ice lake, when you hit the brakes, if your goal is to stay in straight path with no spinout, which wheels would you choose to have locked: front or rear? ...
2
votes
2answers
160 views
Foucault pendulum
The equations of motions for a Foucault pendulum are given by:
$$\ddot{x} = 2\omega \sin\lambda \dot{y} - \frac{g}{L}x,$$
$$\ddot{y} = -2\omega \sin\lambda \dot{x} - \frac{g}{L}y.$$
What are the ...
4
votes
2answers
92 views
Thrust center in space
I have this dilemma: Suppose you have a space ship somewhere in deep space, where there is no drag force or substantial gravity. If the ship has a single engine situated in such a way that the center ...
2
votes
1answer
189 views
Is angular momentum always conserved in the absence of an external torque?
Consider either the angular momentum of the earth around the sun or equivalently swinging a ball horizontally on a string.
I know that with respect to the point of rotation of the swinging ball, ...
1
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0answers
62 views
Limitations on the choice of axis of rotation regarding rolling wheels
Consider a situation where a wheel is rolling without friction on a level surface. Call the center of the wheel $C$, the point where the wheel contacts the ground $G$, and some arbitrary other point ...
6
votes
0answers
100 views
Nuclear Magnetic Resonance (NMR) Conceptual Questions
Let $M$ be the magnetic moment of a system. Below are the Bloch equations, including the relaxation terms.
$$\frac{\partial M_x}{\partial t}=({\bf M} \times \gamma {\bf H_0})_x-\frac{M_x}{T_2} $$
...
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2answers
233 views
What is the proof that a force applied on a rigid body will cause it to rotate around its center of mass?
Say I have a rigid body in space. I've read that if I during some short time interval apply a force on the body at some point which is not in line with the center of mass, it would start rotating ...
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1answer
783 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, ...
2
votes
1answer
99 views
Transform torque from Euler angles to infinitesimal Cartesian rotations
For a certain pair of rigid bodies, I have the gradient of energy in terms of Euler angles. I want to transform this gradient to the gradient of energy in terms of rotations about the $x, y, z$ axes ...
2
votes
2answers
445 views
What causes precession or nutation in a spinning object?
What causes precession in a spinning object?
What causes nutation in a spinning object?
What causes a top, gyroscope, and the earth to wobble?
Just because it's a simple question, I'm not ...
2
votes
5answers
163 views
Forces acting on a point mass in a spinning rigid body
I have learned that all spinning objects will continue spinning even if no force is acting on it, and the tendency to do so is called moment of inertia. But I wonder about the fact that a single point ...
4
votes
2answers
248 views
Which is the axis of rotation?
This should be simple, but it keeps bothering me. If a rigid body has no fixed axis, and a torque (defined relative to a point $A$) is applied, it will rotate around $A$. But often I can also ...
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0answers
249 views
Neglecting friction on a pulley?
So, this is how the problem looks:
http://www.aplusphysics.com/courses/honors/dynamics/images/Atwood%20Problem.png
Plus, the pulley is suspended on a cord at its center and hanging from the ceiling.
...
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0answers
98 views
Forces on hinge point [closed]
A rod of mass M and length L is initially vertical and is hinged about a point $P$. The point $P$ moves horizontally with acceleration equal to $g$, where $g$ = Earth's gravitational pull . Find the ...
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0answers
47 views
Fading transition and rotation of and object in 2D
I'm looking for sources about I guess dynamics subject.
The model I'd like to solve is reduced to a question of:
How does a force applied on a certain point of an object results in both fading ...
2
votes
1answer
82 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 ...
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0answers
66 views
Help course exercises vol.1 Cap Berkeley. 6 [closed]
1 2. Angular momentum of tetherball. The object of the game
tetherball (Fig. 6.24) is to hit the ball hard enough and fast
enough to wind its tether cord in one direction about the
vertical post to ...
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0answers
301 views
How to find Rotational and Translational Equilibrium of Hanging Masses on a Bar?
I am making a hanging mobile which needs to be done mathematically by calculating torque. The problem is, I can't seem to figure out how to solve for the distance of the two masses from the pivot ...
1
vote
1answer
182 views
Non-commutative property of rotation
Addition of angles are non-commutative in three dimensions. Hence some other angular vector quantities like angular velocity, momentum become non-commutative. What is the physical significance of this ...
0
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3answers
267 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.
...
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3answers
582 views
What determines the direction of precession of a gyroscope?
I understand how torque mathematically causes a change to the direction of angular momentum, thus precessing the gyroscope.
However, the direction, either clockwise or counterclockwise, of this ...
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0answers
242 views
Rotational Dynamics Problem-Rod slipping against block
A uniform rod of mass m and length l is pivoted at point O. The rod is initially in vertical position and touching a block of mass M which is at rest on a horizontal surface. The rod is given a slight ...
11
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5answers
798 views
What causes the back of a bike to lift when the front brake is applied?
What causes the back of a bike to lift when the front brake is applied? (Like in an endo.)
Also, if I were to replicate this effect with a wood block with wheels that crashes against a wall (only the ...
0
votes
1answer
87 views
What happens at the end of Coriolis Deflection
Consider we launch a cannonball due south from a point at 45 degrees latitude in the Northern Hemisphere (e.g the point defined with the co-ordinate system on this diagram). The cannonball travels for ...
2
votes
1answer
240 views
Why is an electric motor more efficient at higher loads?
My question is driven by the plot below. We see that acceptable operating range of a motor is between 50-100% of the rated load. Below 40% or so the efficiency of the motor drops off dramatically.
...
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3answers
101 views
Why is $F = mg - T$ in this case?
The situation is as follows:
I am told that $F_{net} = mg - T$ in this case, but doesn't that not take into account that $T$ isn't applied to the center of mass? Newton's second law is defined for ...
