# Tagged Questions

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

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### 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!
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### 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 ...
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### 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 ...
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### 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 ...
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### 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 of ...
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### 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 ...
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### 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 ...
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### 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 ...
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### 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 ...
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### 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 ...
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### 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 the ...
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### 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 ...
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### 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 ...
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### 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 ...
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### 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 ...
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### 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 ...
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### 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 ...
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### 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 ...
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### 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 ...
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### 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 ...
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### 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 ...
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### Relation between linear and rotational motion of molecules?

The temperature of a substance, such as an ideal gas, can be related to the root mean square speed of the molecules. For example, for gases the molecules travel at about 480 meters per second. If we ...
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### Question on relative angular acceleration

I want someone to kindly check whether I am doing (understanding) the math correctly or not. So, let's consider two bodies with constant angular velocities $\omega_1 \hat y$ and y $\omega_2 \hat x$ ...
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### Does the centrifugal force affect stationary objects as seen from the inertial reference frame?

If an object is moving at the same speed as a rotating/accelerating frame of reference it's in contact with but in the opposite direction (making its displacement zero), would such an object be ...
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### How does angular velocity transform on the surface of a sphere?

If we consider the earth as a sphere than it will have an angular velocity of $\boldsymbol{\omega}=\omega\mathbf{e}_z=\frac{2\pi}{T}\mathbf{e}_z$ where $T\approx24h$. Now we have given a location in ...
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### Magnitude of Normal Force in Circular Motion

In the above diagram an object is in vertical circular motion. At $T_0$ the object is at pos1, and at that position, I have shown the forces resolved. So $F_n-mg\cos(a)$ is the centripetal force ...
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### Solid Body Rotation: ω in radians/second or rotations/second?

I am just wondering if I use the solid body rotation equation rotational energy = 1/2mr^2ω^2 and I solve for ω, and then plug in numbers, does the ω come out in radians/second, in rotations/second, ...
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### Angles of rotation

I am haunted by a problem of angles of rotation. Here's my nightmare. At the origin of an inertial frame $R_0(XYZ)$, there is a rigid ball. Another reference frame $R(xyz)$ is fixed to the center of ...
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### Why doesn't this differential derivation of the centripetal acceleration formula work?

I wanted to derive centripetal acceleration from scratch and tried using differential equations. But no matter what I did I hit a snag as follows: $\alpha=$ centripetal acceleration $\omega=$ ...
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### Doesn't rotational KE of a rolling marble change if there is no friction to provide torque?

The question arise from the following situation: A marble at the border of a uniform bowl begins rolling within it from rest. There is enough friction in the first half the bowl for the marble to not ...
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### Man on a rotating platform [closed]

A platform rotates in counterclockwise with angular velocity w. A man walks from the center of the platform to the border with constant radial velocity v' wrt the platform. $\mu_s$ is the static ...
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### How fast does a long object bent at the center need to be travelling in order to boomerang?

At an angle, of course. Standard pressure, average temperature, and calm wind. Bonus question: Can an object that is not bent boomerang at all? If yes, how different would the equations for this ...
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### Angular velocity when a rod inclined to a wall slips and its subsequent motion observed from the axis of rotation

When a rod inclined to a wall slips, rate of change of which angle does the angular velocity represent? Is it the rate of change of angle with which the rod is inclined to the horizontal ? I'm not ...
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### Trying to understand the physical intuition on finding/deriving effective rotation radii of a rigid body

This question is inspired from the answer of this If the rolling is assumed to be without slipping, we can solve the problem by conservation of energy:  mg \Delta h = \frac{1}{2}mv^2 + \frac{1}...
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### To prove uniqueness of Rotation Tensor [closed]

How can you prove that a rotation tensor which rotates some given vector is a unique tensor? Let's say we have a vector 'a' and we take a tensor product of that vector with some tensor 'Z' such that: ...
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### Why does an ice hockey stick, when thrown on ice always rotate and translate together before coming to rest? Why not only rotate or only translate?

When a hockey stick is thrown on ice it simultaneously rotates and translates before stopping. Friction probably plays the main role here, along with the shape of the stick. I think maybe it is due to ...
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### Cause of centripetal acceleration in a ring

Suppose a ring is rotating in space with an angular velocity $\omega .$ Then each element of the ring is having an acceleration of $m\omega^2 r$ ($r$ is the radius of the ring) but what force is ...
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### Parallel axis theorem non-uniform density [closed]

The parallel axis theorem says that if the moment of inertia of a body rotating about the body's centre of mass is $I_{cm}$, then the moment of inertia of the body rotating about an axis parallel to ...
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### Angular Velocity of Semicircle [closed]

In a 2-Dimensional world, a semicircle with center O, mass M and radius r is placed on the ground, with C as the point of contact. A small beetle of mass $m$ is placed at C which starts walking ...
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### Can the average length of the day and night of a planet be different?

At one point in "Marvel's Agents of S.H.I.E.L.D.", some agents are on a planet where the day, defined as the length of time where the sun shines on the planet, occurs only once every 18 years for a ...
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### What are our limitations on spinning a baseball sized 5 kg sphere to really fast speeds?

I know the limitation of the ball being able to hold itself together, lets assume that would not be an issue. If we were to apply a constant force over long enough time would anything short of the ...
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### Rotational kinematics [duplicate]

A particle is moving on a circular path with constant speed. Which of the following is true? (a)it posses radial acceleration. (b)it posses radial velocity. (c)it posses tangential acceleration. (...
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### Earth moves how much under my feet when I jump?

If I'm standing at the equator, jump, and land 1 second later, the Earth does NOT move 1000mph (or .28 miles per second) relative to me, since my velocity while jumping is also 1000mph. However, ...