All Questions
Tagged with velocity rotational-kinematics
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Linear velocity on a circle
Consider a ball rotating around the z-axis with constant angular velocity $\vec{\omega}$, then the linear velocity $\vec{v}$ is given by $\vec{v} = \vec{\omega} \times \vec{r}$. It is easy to ...
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Average angular velocity and speed
Are the magnitude of average angular velocity and the value of the average angular speed always same? If not then can you please give an example.
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Linear and angular velocity of a falling rod in the corner of a room [closed]
A uniform rod of length l and mass m is sitting vertically in a frictionless environment in the corner of a room, having a floor beneath it, and a wall to its left. It gets slightly off balance and so ...
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Does it actually make sense to talk about velocity of the point of contact of a wheel rolling without slipping? (Differentiability of cusps)
I was reading this answer where I saw the following gif:
We can see that when a point becomes point of contact (i.e: touching the ground), the curve of it's motion has a cusp. To my knowledge, a cusp ...
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Is the derivative of the magnitude of a position vector the speed? Is the integral of the speed the magnitude of a position vector?
I'm reading a book titled "Introduction to Mechanics" by Kleppner, and I came across an example: A bead moves along the spoke of a wheel at constant speed $u$ meters per second. The wheel ...
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Tangential velocity - Spherical coordinates
In a spherical coordinates system ($r$, $\theta$, $\phi$ ), assuming an angular rotation $\omega_z$ around the z-axis, the tangential velocity of a point can be expressed as:
$$V_x = -\omega_z R \sin\...
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Need for velocity as rate of change of displacement
Think of the following 2 cases:
An object is in rotation. Take a quarter arc of a circle. The initial and final points of that quarter arc are $A$ and $B$. if we have the arc length as $l$ and time ...
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If an object stays afloat in air for long enough, will it start moving backward eventually? [duplicate]
Let's say, for example, if a helicopter that has an unlimited fuel supply and everything else needed to stay functional stays afloat in air for long enough, would it eventually start moving backwards? ...
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Why doesn't $v_T = \omega r$ involve the direction of its variables?
We derived $v_T = \omega r$ by the following procedure, and it's said that $v_T = \omega r$ "is a relation between the magnitudes of the tangential linear velocity and the angular velocity". ...
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How exactly are linear and rotational velocity and acceleration related?
I understand that distance is always a postive number, so its derivative, speed, is also always positive. However, for rotational motion with angles, it seems that $\Delta \theta$ can have a sign, ...
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Velocity of a car relative to the center of the Earth
If we approximate the Earth's circumference to be $40,075\;km$ we could say that the the amount of time it takes for a full rotation is about $24\; hours$. We could then approximate the rotation of ...
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How do we implement the speed differential for the Ackermann steering?
I'm working on a vehicle that uses four independent motors to control both the steering and speed for each wheel. I'm using Ackermann steering, and I've already got the steering angles down for the ...
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A 1 meter radius ring spins around its axis at 10 revolutions per second. It is now dropped to the ground [closed]
A 1-meter radius ring spins around its axis at 10 revolutions per second. It is now dropped to the ground, where it rolls steadily in a straight line. Assuming it does not lose any energy to friction, ...
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Is there a difference in terminology between velocity vs velocity of the center of mass?
I was wondering if there was a difference between velocity of the center of mass of an object vs finding the velocity of an object in general. The case I was looking at was in a ball rolling without ...
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Angular acceleration of ball when falling [duplicate]
Why is it assumed that angular acceleration is 0 when a ball is midair after rolling off a surface with constant velocity?
