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Questions tagged [rotational-dynamics]

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

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How to find the acceleration of a spool pulled by a force and its work?

I need some help with this problem: A spool with thread wound on it, of mass $m$, rests on a rough horizontal surface. Its moment of inertia relative to its own axis is equal to $I= \gamma mR^2$ ...
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2answers
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Torque Equation

There are two torque equations. and I'm confused about when to use which one given a certain scenario.
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1answer
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What is the direction of rotation of sphere on plank if a force is applied on the plank?

Suppose a solid sphere is kept on a rough plank , and then a horizontal force F is applied on the plank. Then in which direction will the sphere start rolling , given that no slipping takes place , ...
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Concept of polarization in microwave rotational spectroscopy

I am trying to understand the concept of polarization of molecules after they are excited by a microwave pulse. The context is: The complexes are produced in a pulsed supersonic jet expansion of a ...
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1answer
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Homogeneous cube rotating around its edge [on hold]

I'm trying to solve the following problem from the book "Analytical Mechanics" by Nivaldo Lemos: Given the cube above, rotating around the edge that coincides with the z axis, find: i) Vector ...
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1answer
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Rotational Motion (angular momentum)

I don't understand why the angular momentum remains constant even after the distance of the particle (from the origin) keeps on increasing. Maybe I'm not reading the graph the way it is but I don't ...
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1answer
21 views

Velocity of a rotating wheel with axle unlocked from wheel vs locked

For a bike wheel rolling down an incline as like the image, initially the axle of the wheel is not locked to the wheel, so the axle rotates as it moves down the incline but the wheel itself possesses ...
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1answer
28 views

Rotation matrix product and angular velocity

I'm solving the following problem from the book "Analytical Mechanics for Relativity and Quantum Mechanics" by Oliver Davis Johns: Let $R(t)=R_a(t)R_b(t)$ be a rotation matrix. Show that the ...
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1answer
43 views

Confusion regarding rolling without slipping

I'm trying to solve the following problem: Where the rolling uniform disk of mass $M$ and radius has initial velocity of $v_0$ and angular velocity $\omega_0$ (it is rolling without slipping, but the ...
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Velocity of a spool of string being pulled [on hold]

The question given is In working this, I assumed that it was in pure rolling motion and as such friction was negligible. Working through, I found $ ΔKE = \frac{1}{2}Iω^2 = \frac{1}{2}I\frac{v^2}{R^2}...
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Is there a motor design where a rotor gradually moves into a stater? [on hold]

I was wondering if there is a motor/generator design where the rotor moves gradually in and out of the stator along the axis of rotation, or the stator over the rotor, but the primary motion is rotary,...
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Particle rotating about a vertical axis [closed]

A particle is rotating about a vertical axis in the horizontal plane such that the angular velocity about the axis is constant and is equal to 1 rad/s.Distance of the particle from axis is given by R=...
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If net force on a system of particles is zero, torque is independent of the choice of origin [closed]

Can we just prove the above result using these general notations as shown in the figure? I Don't get any idea about how to proceed, help please.
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Calculating the work done on a rotating cylinder by friction [closed]

There's a cylinder on top of a incline with constant friction, and it both rolls and slides down when let go of. How would I calculate the rotational work and the negative friction (heat, sound, etc.) ...
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1answer
41 views

Duration of rotating and sliding down an incline [closed]

A cylinder and a square cube, both with the same mass, are placed on top of an incline with friction and then let go. The cylinder rolls down without sliding, while the cube slides. They arrive at the ...
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2answers
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Axis of rotation of the earth

It is known that the axis of rotation of earth is tilted with respect to the perpendicular to the plane of orbit. Is there a way to measure this tilt from earth without the aid of pictures taken from ...
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1answer
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Why is translational energy part of the equation for kinetic energy for the first leg of a double pendulum?

Isn't all kinetic energy of the first leg already in the rotational energy based on the angular velocity theta_1_dot? https://en.wikipedia.org/wiki/Double_pendulum#Lagrangian (i'm referring to 1/2*m*...
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2answers
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Angular momentum of a body about a point rotating about its own axes

I want to calculate angular momentum of a sphere about point O. The sphere is rotating about its two axes with angular velocities $w_1$ and $w_2$. I know that angular momentum = $m\vec{r}\times\vec{v}...
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2answers
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How does changing radius (constant mass) affect rotational kinetic energy?

I'm trying to understand how rotational energy would change if radius shrinks but mass stays the same. The initial question was posed as follows: "The radius of a disk of matter forming around a ...
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2answers
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An illogical argument in Goldstein while deriving the Euler's equation(s)

In the book of Goldstein, at page 200, the author argues while deriving the Euler's equation(s) that $$\left.\frac{d\vec L }{dt }\right|_s = \vec \tau,$$ where subscript $s$ denotes the space frame. ...
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1answer
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Why does plate need an external torque to continue its rotational motion with constant angular velocity?

Consider the following question: a-) By using the principal axis frame, calculate the torque needed to rotate a rectangular plate with sides a and b about its diagonal with a constant angular ...
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Hiw to find net frictional force if the surface in contact are rotating w.r.t. each other [closed]

A disc of radius R is kept flat on a rough horizontal surface of friction coefficient μ with its axis vertical. It is given an angular velocity ω about its vertical axis and horizontal velocity v(v
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Do rolling objects “weight” more?

We know that whenever an object is supported by a surface, the gravitational force on the object is countered by the supporting force of the surface. Assume an object is rolling without slipping. ...
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1answer
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Kinetic Energy Comparison Marble Question

A uniform marble of mass M rolls down a symmetric bowl, starting from rest at the top of the left side. The top of each side is a distance h above the bottom of the bowl. The bowl is rough enough to ...
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1answer
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Effect of spin on the deflection of a rigid body

Suppose an x-y coordinate axes is set on the ground, then a spherical object is projected in the forward direction (the positive y direction) and while moving in this forward direction it also ...
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Rotational potential energy on a system of two masses

On a homework assignment, we were given the following problem: This system is held at equilibrium according to the configuration in the image; initially the body B is at rest, and the body A is ...
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1answer
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Moment of Inertia of a semi ellipsoid?

I understand that mass is simply found by taking the integral of $\rho$ and differential volume. I just do not understand how you can take the del of $I_x$ and where that equation $y^2\text{d}m/2$ ...
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When talking about the rolling of an object (such as a wheel) what is the difference between sliding and slipping?

My question is rather simple. Concerning with the rolling motion, what is the difference between slide and slip?
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1answer
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Circular motion of a ball suspended from the rim of a rotating table [closed]

Susppose there is a ball with radius $r$ suspended to the rim of a circular spinning table with radius $R$ by a string with length $l$ which makes an incline angle $\theta$ with the vertical axis. If ...
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1answer
39 views

Billiard ball with side spin

A cue ball is travelling along a snooker table. Initially, it has only side spin (yaw). As it travels it will develop a rolling spin (pitch). Can the ball develop any (roll) and thus move off the ...
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2answers
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Cylinder on the bed of a truck, rolling without slipping

I tried to solve a physics problem that involves a cylinder on a truck that is accelerating. I'm supposed to solve the acceleration of the center of mass of the cylinder when the acceleration of the ...
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3answers
46 views

Can we know when rolling occurs without slipping?

In school we solve a lot of physics problems involving rolling cylinders/hoops/wheels. Often it is specified in the question statement that "rolling can be assumed to occur without slipping". Then we ...
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1answer
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How is high tide related to tidal bulge?

This is going to be a basic question. But I'm confused at the conceptual level.. The following is a popular diagram explaining the tides: I understand why the bulges appear on the right and left ...
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1answer
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What is the physical argument for $d(G)_s = d(G)_b + d(G)_{rot} \quad ?$

In the book of Goldstein, Classical Mechanics, at the end of the page 171, it is stated that A relation between the two differential changes in $G$ can be derived on the basis of physical ...
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1answer
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Rotation of water inside closed solid sphere

Is there any way to determine the volume of a sphere of water contained inside a solid spherical shell(of known thickness but unknown radius) by studying the rotation of the whole sphere(solid shell ...
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1answer
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Flywheel regenerative braking - gearbox

If you were to use a completely mechanical flywheel (i.e. no use of a motor-generator) to use in a regenerative braking system, would the gearbox be responsible for controlling the "charging" and "...
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1answer
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Angular Momentum and assymetric axis

The question I came across , If a semicircular disc rotates uniformly (const. angular velocity) about an axis passing through its Centre of mass , and prependicular to its plane , do we need an ...
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3answers
53 views

Rotational KE vs Translational KE [closed]

Q. Horizontal electric field E = mg/q exists as shown in the figure and a mass m is attached at the end of a light rod. if mass m is released from the position as shown in the figure. find the angular ...
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Angular Impulse equations for rotational dynamics

Consider a 3d rigid body at rest initially, assuming no net external forces acting on it. It is set in perpetual rotation along one of its principal axis. Now an angular impulse (which is a vector) ...
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2answers
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Perpetual Rotation of Rigid Body

Assuming no external torque or forces acting can a rigid body be set in perpetual rotation motion about an axis which is not its principal axis? If no then does the earth continuously change its ...
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1answer
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Rolling on a track in vertical plane

A sphere of mass m and radius r is released from rest at point A on a track in vertical plane. The track is rough enough to support rolling between A and B and from B onwards it is smooth. My ...
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3answers
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Do objects rotate around their center of mass or not?

I read this question on why objects tend to rotate around their center of mass. The accepted answer said that objects in general do not rotate around their center of mass. I'm confused about this. I'...
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Rotational mechanics collision problem of a rod and body [duplicate]

Smooth ball of mass m moving with a uniform velocity 0 v strikes a smooth uniform rod AB of equal mass m , lying on a frictionless horizontal table. The ball strikes the rod at the end A, ...
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1answer
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inertia tensor of rigid body in generalized coordinate frame?

Assuming we know the inertial tensor of a homogeneous rigid body about a coodinate frame at its COM and aligned to it principal axes, how do we find the inertial tensor for the body in some other ...
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1answer
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A horizontal plank is moving towards right over a system of 3 roller drums as shown .the ratio of transilational spped of smaller and larger drum [closed]

the ans for 21st is 1A horizontal plank is moving towards right over a system of 3 roller drums as shown .the ratio of transilational spped of smaller and larger drum
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5answers
70 views

Effect of earth's rotation in ballistics

For this purpose, let's consider earth's rotations constant. Do earth rotation momentum get transfered to any object (a missile for example) that get's lauched? If so, why do we have to consider earth ...
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0answers
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Work done by frictional force when rolling without slipping [duplicate]

When an object is rolling (no slipping) on a slope there should be a frictional force which causes rotation. But when we use power insulation philosophy, we haven't considered about an energy loss ...
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A surface where velocity is not equal to the product of angular velocity and Distance vector R

I am trying to imagine a setup where pure rolling is taking place, the COM is definitely moving with a linear speed , say $v$, but the relation $v= \omega × R$ does not hold good. Is there any setup ...
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No friction in pure rolling - how about driving a car?

I remember the un-intuitive result that pure rolling without acceleration involves no friction by the law of conservation of angular momentum. Conjectures: I understand that when I'm driving a car at ...
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3answers
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Moment of Inertia Race [closed]

Wikipedia shows an example of how to the moment of inertia determines how fast a rotating object rolls down an incline plane. the race Includes: spherical shell, solid sphere, cylindrical ring. solid ...