Questions tagged [rotational-dynamics]

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

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3answers
42 views

Finding Direction of Angular Velocity

Suppose I have a 3D rigid object on which some external forces act at various points located on it. The resulting motion would, in general, be the translation of center of mass plus rotation about the ...
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2answers
85 views

Is it possible that this electromagnetic field propulsion system would not violate any conservation laws? [on hold]

I have recently come up with a design of a conceptual electromagntic field propulsion system which should not violate any conservation laws, particularly the Law of Conservation of Momentum and the ...
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0answers
33 views

Rotational inertia [on hold]

Consider two bodies, A and B, of equal mass set at a short distance. Body A is spinning and body B is at rest. Then, through some kind of electromagnetic device, a strong repulsive force is ...
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0answers
41 views

Which of the following is not conserved ( for the following options) [on hold]

A smooth tube of certain mass is rotated in gravity free space and released. The two balls shown in the figure move towards ends of the tube. For the whole system which of the following quantity is ...
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0answers
31 views

The exact location of normal force and friction vectors [on hold]

I am struggling with a following question: "A cylinder of radius $r$ and height $h$ is standing on an inclined plane pitched at an angle $\theta$ to the ground. Given the coefficient of friction $\mu$ ...
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0answers
23 views

Toilet Paper roll [on hold]

Why we don't replace R in formula (RT=(1/2)m(R2+r2)(a/R)) into (R,outer diameter +r,inner diameter)? Does the inner roll also rotate?
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1answer
42 views

Inverted pendulum, EOM

Consider the inverted pendulum shown below: where $F$ is an external force, $B$ is the CoM of the rod, $A$ is the position of the joint where the rod attaches to the car. Angles increase in the ...
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0answers
27 views

The problem was found in the book of mechanics by Kleppner and Kolenkow [closed]

If you start a coin rolling on a table with care, you can make it roll in a circle. The coin leans inward, with axis tilted. The radius of the coin is 'b' the radius of the circle it follows is R and ...
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0answers
26 views

Angular velocity in body frame [closed]

I am reading about IMU and getting confused in term "angular velocity of body frame with respect to Inertial frame introduced in body frame". It is said in text it is measured by IMU. If someone ...
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1answer
23 views

Moment of Inertia Tensor Terminology

I've learned about the moment of inertia tensor as a matrix that can be used to compute angular momentum, moment of inertia, etc. for a system. But why is it often described as a tensor instead of a ...
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1answer
43 views

Finding net torque from dimensional torques

$F = ma$, and if I have acceleration vectors in 3D it's easy enough to just find $|a| = ||a_x + a_y + a_z||$, so I can find |F| = m|a|. Great. How can I do the analogous thing with rotational vectors?...
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0answers
30 views

Does an object with an axially symmetric inertia tensor have a “preferred” axis of rotation?

Imagine an object with cylindrical symmetry, such as a cylinder or cylindrical shell, where $I_{xx} = I_{yy} \neq I_{zz}$, and the Z axis is defined along the length of the cylinder shape. The object ...
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0answers
15 views

Circular Motion and Force [closed]

The maximum breaking strength of a piece of cord is 250 N. What is the maximum rpm at which the line can retain a 3 kg mass swung in a 1.8 m radius circle?
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1answer
35 views

If $v_{contact,road}$ in rolling motion is zero, how the contact point still manages to move forward? [duplicate]

If velocity of contact point of a rigid body performing rolling motion w.r.t road is zero then how the point gets delocalised from its initial position after some time? My textbook says, At any ...
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0answers
17 views

Difference between types of “reference” in second order ordinary differential equation

I'm looking at a second order ODE (wrt time $t$) from power systems defined as: $$ M \,\ddot{\delta}_i = P^m_i - f^e_i(\delta) - D \dot{\delta}_i \tag{1} $$ for $i \in 1, \ldots, N$ where $f^e_i(\...
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0answers
41 views

How does friction cause a spinning top to fall?

I am wondering how friction can create a torque to change the angular momentum and cause a spinning top to tilt, like in the diagram of a close up of the rounded tip of a top while the angular ...
1
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1answer
32 views

Do we take torque/angular momentum about a point or an axis

It has left me a bit confused, because at some places the angular momentum/torques is taken about a point , while in others, its taken about an axis. Consider the 2 situation. Question 1:In a conical ...
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0answers
24 views

Free body diagram [duplicate]

I was reading about the ABS brakes and the articles say the wheels don't slide on the floor and the tire friction is static. but what would the force diagram of a tire look like under ABS? Wouldn't ...
2
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2answers
40 views

Strategy for a person throwing an object in zero G to maximize a velocity

If an astronaut is drifting away from a space station holding a wrench, they could throw it in the opposite direction in an attempt to get back. But if they do it wrong, they will only end up ...
2
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3answers
40 views

On moment of inertia calculation of a triangle

I have seen multiple videos on YouTube which start off the process of calculating the moment of inertia of a triangle about it's base by writing it equal to  $\int(y^2\ dA )$ where $y$ is the ...
0
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1answer
22 views

A pendulum stuck on a horisontal slider and jamming

I'm wondering if my idea of conservation of energy is correct when it comes to a pendulum attached to a slider, and what happens during a jam. I have worked out the equations of motion, and assuming $...
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1answer
27 views

Energy of Rod about pivot

Consider a rod, with mass $m$ and length $l$, that is fixed about a pivot point at one of its ends. Now imagine that we flick the rod so that the end of it attains a velocity of $v_{0}$. Now, if we ...
0
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1answer
26 views

A thin rod is standing on a smooth surface [closed]

A uniform thin rod of mass m and length l is standing on a horizontal surface. A slight disturbance causes the lower end of the rod to start falling. find the velocity of the centre of mass of the rod ...
0
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1answer
34 views

Coordinate Transformation of Torque

According to angular-velocity-expressed-via-euler-angles you can express angular velocity in euler angles. Would the coordinate transformation be the same if I were to convert torque vector $\vec{\tau}...
2
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5answers
86 views

Does the law of conservation of momentum mean both linear and angular momentum?

I was solving a problem where a bullet hit a rod hinged about one of its ends. The rod is standing vertically before the collision. We had to find the final angular velocity of the rod. The way we did ...
2
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1answer
44 views

For a physical pendulum, why do you use an angular coordinate system when the centre of mass translates too?

I am trying to understand why you can use $F=ma$ for a simple pendulum, yet need the rotational equivalent for a physical pendulum. I understand it is because the rigid body can rotate too, whereas ...
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0answers
30 views

What are the conditions that an asymmetric top will perform precession in space (zero torque)?

The conditions that an asymmetric top will perform precession under gravitational field are described in the article Precession of an Unsymmetrical Top. (I can't get the full article.) But what if ...
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1answer
27 views

How to calculate the moment of inertia of a cut out portion?

So, I have watched a lot of videos on YouTube, whereby if there is a portion cut out from a particular shape (mind you the that the shape is more often that not symmetric), then the moment of inertia ...
2
votes
2answers
48 views

What is the exact role of friction in rolling without slipping?

When an object rolls along a plane, we say that for the object to roll without slipping, the velocity of the center of mass must be equal to angular velocity times radius, so that at the point of ...
4
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3answers
112 views

Every action has an equal and opposite reaction. Is is true for torques as well?

So, we studied in classical mechanics that every action has an equal and opposite reaction. So if we apply a force to some object, that object will exert an equal amount of force on us but in the ...
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2answers
63 views

Acceleration of the centre of mass of a hinged rod [closed]

This is a freely falling rod of mass m and length L hinged at one end. I have to find the acceleration of its centre of mass. 1) I don’t think its acceleration can be greater than g in any case as ...
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1answer
88 views

Why $\int_m \left( y^2 + z^2 \right)dm \neq \frac{1}{3}mL^2$?

for a cylinder, let's say with constant density with radius $3$ and height $10$ so $$ \rho(r, \theta, y)=1 $$ so $$ dm = \rho\left(r, \theta, y\right)r \, dr \, d\theta \, dy = r \, dr \, d\theta \, ...
2
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1answer
101 views

Rigid body dynamics: modelling a polygon bounce off ground

I'm currently making a physics simulator, but I'm having some trouble making a polygon bounce off the floor. I know that collisions are normally modeled as described below by ja72, but I did it ...
0
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3answers
71 views

Contradiction in Euler rotation Equation

By Euler rotation Equation, torque $$\tau (t)=I \omega '(t) + \omega(t) \times I \omega(t)$$ where $I$ is the inertia tensor in rotating frame and is constant; $\omega(t)$ is the Angular velocity in ...
1
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1answer
59 views

Conservation of Kinetic Energy?

A rod is hinged in a vertical plane. If we throw a ball at the rod's lowest point with some velocity, and they undergo elastic collision, can the total mechanical energy be conserved? What about the ...
2
votes
1answer
94 views

How does conservation of momentum apply to this billiard ball problem? [closed]

A billiard ball, initially at rest, is given a sharp impulse by a cue. The cue is held horizontally a distance $h$ above the centerline as in the figure below. The ball leaves the cue with a speed $V$ ...
1
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1answer
66 views

Tensors time derivative in moving frames

I know that the following relation exists between the time derivative of a proper vector "v" in an "absolute" frame A and the time derivative of the same vector in a "relatively moving" frame B: $$ \...
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0answers
32 views

Does the torque in the Euler's rotation equations is taking along the world frame or the rotating frame?

Euler's rotation equations state that: M=Torque=IW'+WXIW where W,W',I are taking along the rotating reference frame is M also taking along the rotating reference frame?
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3answers
56 views

Rolling without slipping forward force

I'm studying rolling without slipping, I want to find the net force making a wheel go forward when applying a torque about the axle of the wheel. In this page https://www.school-for-champions.com/...
0
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1answer
27 views

Co-rotating body frame

I have a question that has been bothering me for some time. Imagine we have a bunch of point masses and two frames, the laboratory frame and a frame wich is located at the center of mass of the bunch ...
1
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2answers
67 views

Moment of inertia for a random polygon

Is there an easy way to calculate the moment of inertia of an arbitrary 2-dimensional polygon, with respect to an axis perpendicular to the plane of the polygon (passing through the center of mass)? ...
0
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1answer
50 views

Friction in opposite directions on a rotating disc [closed]

A disc with radius R rotates at constant angular velocity $ω$. At time $t=0$ a person steps onto the disc at point $A$ and moves at constant velocity $V$ (with respect to the rotating framework) to ...
3
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3answers
102 views

If an rod is hit at its edge with an impulse I, why would it move with the same velocity as if it were hit at its center?

In one of his lectures, Walter Lewin gives the example of a rod which is hit with an impulse on its edge. It starts rotating with angular velocity w, and its center of mass moves with velocity v. ...
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1answer
21 views

How much lateral acceleration during cornering is needed to flip a car?

I'm doing my IB HL Math Exploration, where I use a bit of physics. Say I have a car with mass m, center of gravity at height h, and width of 2b, and I am turning a corner, how much centrifugal ...
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4answers
3k views

Why are angular mometum and angular velocity not necessarily parallel, but linear momentum and linear velocity are always parallel?

I have read that it's not necessary for angular momentum and angular velocity to be parallel, but it is necessary for linear momentum and linear velocity to be parallel. How is this correct?
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1answer
36 views

Total Angular Momentum of system of particles

In my mechanics book while working out the total angular momentum's formula analogous to the center of mass of the system from the fig it concludes $r_i=R+r_i'$ Taking derivative $v_i=V+v_i'...
1
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1answer
144 views

Does an asymmetric top return to its initial position &orientation, while rotating freely in space? (contradiction in Landau&Lifshitz mechanics book)

The Poinsot's ellipsoid tells us that the angular momentum ($M$) (in the rotating frame) should be lying on the intersection curve between the conservation of momentum sphere radius $|M|$: $M_1^2 + ...
0
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1answer
77 views

Placement of the spaceports on our Earth

Why are spaceports located at certain points (site/place) on our Earth? Is there a physical reason I don't really know about?
0
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2answers
78 views

Why is $\theta=\beta/2?$ - Kinematics [closed]

An aircraft is flying horizontally in a circle of radius $b$ with constant speed $u$ at an altitude $h$. A radar tracking unit is located at $C$. Write expressions for the components of the ...
0
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0answers
19 views

Relationship between the period and the shape,inertia of a wheel

I want to construct a wheel using two metal strips having different physical properties(one over the other),so that it oscillates about an axis perpendicular to the plane of the wheel and passing ...