Tag Info

2

Notice, the linear velocity $v$ is co-related with the angular velocity $\omega$ as follows $$\text{linear velocity}=(\text{radius})\times (\text{angular velocity})$$ $$v=r\omega$$ by setting $v=r\omega$, we get $$T=\frac{2\pi r}{v}=\frac{2\pi r}{r\omega}=\color{red}{\frac{2\pi }{\omega}}$$

2

When initially you exert a force $F_i$ to get things going, you're actually exerting a torque $T$ about the centre point of the circle: $$T=F_i R,$$ with $R$ the radius of the circle. According to Newtonian physics, this torque causes an angular acceleration $\dot{\omega}$ as follows: $$F_i R=I\dot{\omega},$$ where $I$ is the Moment of Inertia of the ...

1

In the ideal case where there is no friction and no perturbations and the top starts to spin in a perfectly vertical alignment, the two configurations (inverted or not) of the top are completely identical. However, once you have the top start rotating with a tilt from the vertical axis, or consider perturbations that will tilt it even if it wasn't, then the ...

1

Their paper is inconsistent. They filled in $\omega = 264$ with the other quantities in SI units, so ω should be expressed in rad/s (often written $\mathrm{s}^{-1}$). So they assumed ω was already in rad/s. If they say they assumed $\omega = 264~\mathrm{rpm}$, that's not consistent with the values they plugged in. Your value of 69696 is hard to decipher ...

1

Its an application of the formula $$\text{Time} = \frac{\text{Distance}}{\text{Speed}}$$. $2\pi r$ is the distance covered in one revolution and $v$ is the speed. In terms of $\omega$ $$T = \frac{2\pi}{\omega}$$. (Also note that $\omega=v/r$)

Only top voted, non community-wiki answers of a minimum length are eligible