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 \(-9.8~\mbox{m/s}^2\).

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

Find 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.

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