Classical Mechanics
# 2D Dynamics

What is the period of rotation (in minutes) of the Earth so as to make any object weight-less on its equator?

**Details and Assumptions**

- The radius of the Earth is $R = 6 \times 10^{6}\text{ m}.$
- The gravitational acceleration is $g = 9.8\text{ m/s}^2.$

**M** and radius **R** is thrown along a rough horizontal surface so that **initially**, it slides with a linear speed $\displaystyle{\upsilon_0}$,but **does not rotate**.
As it slides, it begins to spin and eventually rolls without slipping. The time taken to start rolling can be expressed as $\dfrac{a}{b} \times \dfrac{\upsilon_0}{\mu_k g}$ Where $\displaystyle{\mu_k}$ is the coefficient of kinetic friction between the surface and the ball .What is $\displaystyle{a+b}$?

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The Hyperloop is a hypothetical new fast transport system between cities, which works by launching pods that carry people through a very low air pressure tunnel. While riding in the Hyperloop, some coins fall out of your pocket, taking 1/3 of a second to hit the ground. How much more quickly would the coins have hit the ground if you were sitting still **in seconds**?

**Details and assumptions**

- The radius of the earth is $6370~\mbox{km}$.
- The Hyperloop travels at $300~\mbox{m/s}$.
- When sitting still relative to the Earth's surface, acceleration toward the Earth is $-9.8~\mbox{m/s}^2$.

$0.5$. It is then given a very slight push. It begins to fall off the table.

A solid spherical ball is placed carefully on the edge of a table in the position shown in the figure. The coefficient of static friction between the ball and the edge of the table isFind the angle (in degrees) turned by the ball before it slips.

**Details and Assumptions**

- Find the angle with the vertical.

**meters**?

**Details and assumptions**

- The acceleration of gravity is $-9.8~m/s^2$.
- The spring doesn't squeeze all that much, so you may assume that the vertical angles on the top and bottom remain at $60+\epsilon$ degrees, where $\epsilon$ is a small angle.