A tag for questions about rotational motion, including angular velocity and angular acceleration.

learn more… | top users | synonyms

-1
votes
1answer
46 views

Why is angular acceleration of a pendulum always negative?

I was trying to derive using the Lagrangian the equations of motion of a simple pendulum under the influence of gravity. Eventually, I was brought to this conclusion: $$\alpha = -(g\sinθ)/l$$ where ...
0
votes
2answers
17 views

The direction of frictional force in circular turning

Why does the frictional force in case of circular motion point towards the center even though the motion is tangential to the radius?
0
votes
1answer
36 views

Derivation of centripetal acceleration

While reading HC Verma chapter 7 circular motion I came across a derivation which I couldnt understand. I have marked my doubt with red. I don't understand from where +dw/dt [- i sine +j cos0] came ...
3
votes
1answer
185 views

General motion of a cone on an inclined surface

Suppose that a solid cone is placed horizontally on an inclined surface and is initially at rest. How will the cone move when it starts motion due to its weight? I know that its motion depends on the ...
2
votes
1answer
56 views

Problem on rotation

So this is the problem:A wheel of radius of gyration k is placed on a belt moving with a speed v, which is maintained constant by means of an external agency. Assume that the axis of the wheel is ...
0
votes
0answers
18 views

kinematic constraint of spacecraft

I am now reading a paper about trying to use convex optimization to solve the attitude control of spacecraft. However, I do not have background on the physical part: Let 1. $\omega(t) = ...
0
votes
1answer
27 views

Why do we represent the axis of rotation using vectorial notation [closed]

When a body (in pure rotation) rotates along an axis passing through it, why do we represent the axis of rotation in vectorial notation? Wouldn't it be sensible enough to represent the angular ...
0
votes
1answer
26 views

instantaneous velocity center

The instant center of rotation, also called the instantaneous velocity center is the point fixed to a body undergoing planar movement that has zero velocity at a particular instant of time, ...
0
votes
1answer
30 views

Rotation and Momentum

I understand that according to one of Euler's theorems, any solid object's 3D rotational orientation can be represented by a single 3D vector and an amount, i.e. a 4D vector. However, is it correct ...
-1
votes
1answer
57 views

Vertical circular motion(with gravity)

Let's say I have a stone tied to a string and swing it vertically upwards. Now, if I provide an initial velocity such that the velocity of the stone = 0 at an angle greater than 0 from the ...
0
votes
1answer
73 views

Pendulum question- Angular momentum-impulse

The pendulum of mass m and length l is released from rest at $\theta=0$. Using only the principle of angular impulse and momentum, determine the expression for $\ddot \theta $ in terms of $\theta$, ...
0
votes
1answer
49 views

A vector in a rotating frame. Find the rate of change of this vector ('particular step derivation') [duplicate]

I am doing a project with the fundamental background not in my major. I am reading the following lecture: How to get the green part? Can anyone show me the detailed derivation or provide ...
2
votes
1answer
201 views

To prove uniqueness of the rotation tensor associated with rotation of a rigid body

Suppose there are $N$ particles embedded in a rigid body which undergoes some random rotation such that: $$ \overline{\overline {R}}_{ij} \otimes \vec{a}_{ij} = \vec{b}_{ij}$$ where, $i$ and ...
1
vote
1answer
375 views

Rotational mechanics - ball climbing a step

A wheel of radius, $R$ and weight, $W$ stands in front of a step of height, $h$ where h is less than R. What is the least horizontal force $F$ which must be applied at the axle of the wheel to allow ...
1
vote
0answers
37 views

Why does a fan blade appear to spin backwards when spun really fast?

This a phenomenon which I notice everyday but never really took an interest in. Why does a fan (or any other rotary object), when spinning really fast, 'appear' to slow down, upto a certain rpm, then ...
0
votes
3answers
938 views

Conservation of Angular Momentum, as related to a flywheel

Trying to work out some pesky flywheel dynamics for a project I'm working on, would love some for your assistance to better understand the underlying concepts. For a given flywheel (thin-walled ...
0
votes
1answer
211 views

How does ground interact with a box rotating around its corner?

I have some questions about how forces $F$, friction force $F_{friction}$, and normal $N$ interact in order to the box below to turn (clockwise) about the red corner, without sliding. The force $F$ is ...
1
vote
0answers
45 views

Centripetal acceleration [closed]

I know if a particle is accelerating around the earth it has $$a= \omega*v$$ My question is how do I express this in terms of the unit vector. Would it go something like this. $$|a| = |\omega*v| $$ ...
0
votes
2answers
231 views

Why falling camera/objects rotate and then stabilize?

I was going to ask something very similar to this question (which hasn't been answered). Basically a camera fell from an airplane and it began to rotate (maybe because initially it was put in rotation ...
1
vote
2answers
51 views

What is the purpose of the directions for vector quantities such as angular velocity and torque?

Looking at just both angular velocity and torque, many other exhibit this same property. What is the purpose of and usefulness of having a direction that is in the Z-direction? (assuming that, in the ...
0
votes
1answer
284 views

Kinematics of a differential drive robot

(I am reposting here a question I asked on stack overflow, since it actually sits right in between programming (modeling of 2D physics) and physics proper (kinematics). I think I have the physics part ...
0
votes
3answers
91 views

Centripetal and Centrifugal force

If water stays in a pail of water that is whirled around a circular path, the water stays in the pail. But is it because of centripetal force or inertia? I'm getting confused by all the different ...
0
votes
1answer
118 views

What is intertia tensor for tapered cylinder (solid and with separate inside and outside radii)?

I need the inertia tensor for tapered cylinders, both solid and hollow, and if possible with independent inner and outer radii on the $x$ and $y$ axes (so the cross-sections of the cylinders can be ...
-1
votes
0answers
14 views

Apply torque in 3d [duplicate]

Suppose I have an object with some inertia tensor I and angular momentum l. Suppose I apply a torque t. How does the object's orientation change over time?
0
votes
2answers
40 views

Momentum of a rack and pinion gear system excited by a time variant force

Background I have a rack and pinion gear system as shown in the image below The pinion gear is attached to a flywheel at the back. The first state of the system, none of the gears or the ...
1
vote
1answer
168 views

How to calculate angle of inclination attained by a weigh balance on unequal loading?

Actually I need to rotate the beam (pivoted at centre) with constant angular velocity using the priciple of mass imbalance. Could anyone suggest what would be rate of decrease of mass in one pan ...
0
votes
3answers
48 views

Axis of rotation and rotating rigid body [closed]

We know that angular momentum of a solid disk rotating with angular velocity $\omega$ is given by $I\omega$ about its center. Now if I chose any axis (parallel to above), will it have same magnitude ...
5
votes
1answer
189 views

Rotation of Spacetime $\Rightarrow$ Change in orbit/path

Along the idea of frame-dragging; Will the rotation of a black hole, which has some velocity v and angular momentum, influence its path in 3D space? I've seen the fact that depending on the ...
-2
votes
1answer
30 views

Newton's 2nd law for rotation (accelerated rolling and inertial frame of reference) [duplicate]

I need help in understanding why, in accelerated rolling, the center of mass must be at the origin of an inertial frame of reference in order for the second law to be applicable. Thanks!
0
votes
1answer
44 views

Angular momentum definition? [closed]

The definition of linear momentum is this: Momentum is a vector quantity defined as the product of an object's mass, $m$, and its velocity, $\vec v$. So According to that definition,The definition ...
1
vote
4answers
355 views

Instant centre of rotation for two connected gears

The two gears are have the angular velocities $\omega_1$ and $\omega_2$ respectively with respect to $Oxyz$. The task is to determine the angular velocity $\boldsymbol{\omega}$ of the arm ...
0
votes
1answer
61 views

Friction of a scissor [closed]

How can the friction by a scissor blade be related to its angle? To be more specific this is the question that I came across. A scissor is used to cut a wire of circular cross section and ...
2
votes
5answers
62 views

Two identical disks pulled differently question (Kinetic Energy)

I am currently taking a basic physics course in college and I am having a bit of trouble on this problem that deals with rotational and translational kinetic energy. Let's begin: The question: The ...
0
votes
2answers
53 views

When it is usually taken as $\omega=v/r$, why in this particular case $\omega=v/3r$ is taken?

A circular disc of mass m and radius r is set into motion on a horizontal floor with a linear speed v in the forward direction and an angular speed w =v/3r in clockwise direction .Find magnitude ...
0
votes
1answer
25 views

For a rolling object, is the tangential velocity the same as the velocity of the center of mass?

For example, a solid disk rolling down a hill would include both rotational and linear kinetic energy. For the rotational kinetic energy ($\frac{1}{2}I\omega^2$) the angular velocity becomes $v/r$ but ...
0
votes
2answers
36 views

Why does the angular speed formula end up in radians per second?

So, in my homework I am given the radius and also the tangential speed $v$, the measurement for radius is meters; the measurement for $v$ is $m/s$. I don't understand how by after calculating the RPM ...
1
vote
1answer
42 views

How to find angular velocity of rotated objects in 3D

I am trying to obtain equation for angular velocity of rotated object in 3d. I started with defining yaw, pitch and roll angles. Then I wrote rotation matrices from these angles. As I understand it ...
0
votes
1answer
22 views

Objects rotating and rolling without slipping

The question below confused the hell out of me. It's pretty much straight forward but until the point of where to use which radius. I know that I'll have to use the formula Tr=Iα and then we simplify ...
0
votes
2answers
37 views

Proof derivative of a vector following precession motion

I do not get some points of this proof about the time derivative of a unit vector $\hat{u}$ (costant magnitude) which is following a precession motion. The picture is the following. I want to ...
0
votes
1answer
40 views

Question about friction in rolling without slipping?

I was under the impression that for a ball/cylinder to roll without slip, there must be a static friction force that opposes the direction of motion. Why, in this case, does the friction act in ...
0
votes
0answers
58 views

Kinetic energy of rotating rigid body

Sorry for boring you my friends. I am haunted by a problem of kinetic energy of rotating rigid body. Usually, the kinetic energy is calculated in the attached body reference. Because we could take the ...
1
vote
1answer
229 views

Is displacement in circular motion a chord or an arc?

When taking the displacement between two points along a circular path to calculate its velocity, do you take the length of a chord connecting the two points or do you take the length of the arc ...
0
votes
1answer
32 views

Proof of constant angular velocity in rigid body motion

I'm studying rigid body motion on Landau but I'm having troubles to understand this proof of the fact that the angular velocity $\vec{\Omega}$ is constant for a rigid body. My doubt is about the ...
1
vote
5answers
5k views

Difference between circular motion and rotational motion

Are rotational motion and circular motion different or the same? If different then when can we say that a body is in circular motion, and when it's in rotational motion? I find several answers where ...
1
vote
1answer
42 views

Why will kinetic energy decrease?

Specific situation : A ring of mass M and radius R is rotating about its axis with angular velocity w. Two identical bodies each of mass m are now gently attached at the two ends of a diameter of the ...
1
vote
3answers
45 views

Why the similarity in the Equations of Motion for Rotational and Rectilinear Motion?

These are the equations of motion given constant acceleration, for first rectilinear and then rotational motion. Rectilinear Motion: Rotational Motion: While the variables have changed, and the ...
0
votes
1answer
23 views

Interial Momentium Question

I had a question for my Physics 101 class and was wondering if anyone could share some insights. The question was stated as follows. A pottery wheel of radius 0.5 m and mass 15 kg rotates ...
0
votes
0answers
29 views

Does vehicle tire mass effect efficiency?

This question has an interesting origin: A tire salesman was recommending tires (aka tyres) for a highly fuel-efficient vehicle. He said the vehicle was light (compared to most production cars), and ...
5
votes
3answers
201 views

Could moving land mass alter Earths gravity?

This is potentially a very stupid question but I'm going to ask it anyway. With all these huge buildings such as the Abu Dhabi Mosque, where an unbelievable amount of materials such as marble was ...
0
votes
2answers
85 views

Question on Angular Acceleration and Velocity

suppose, we have a body with an angular velocity, $$\vec \omega=(at,b,0)$$ where $a,b$ are constants. so the angular acceleration is clearly, $$\dot{\vec{\omega}}=(a,0,0) $$ but my question is if ...