A 0.0215 m diameter coin rolls up a 20.0 degree inclined plane. The coin starts with an initial angular speed of 55.2 rad/ s and rolls in a straight line without slipping. How much vertical height does it gain before it stops rolling?

The coin will reach a vertical height of 0.027 meters before it stops rolling.

Explanation:

Let suppose that coin-ground system is a conservative system and begins at a height of zero. Since the coin is experimenting a general plane motion, which is a combination of translation and rotation. By Principle of Energy Conservation we have the following model:

(1)

Where:

- Translational kinetic energy at the bottom of the incline, in joules.

- Rotational kinetic energy at the bottom of the incline, in joules.

- Gravitational potential energy at the top of the incline, in joules.

By definitions of Kinetic and Gravitational Potential Energy we expand (1):

(2)

Where:

- Momentum of inertia of the coin, in kilogram-square meters.

- Angular speed, in radians per second.

- Radius of the coin, in meters.

- Mass, in kilograms.

- Gravitational acceleration, in meters per square second.

- Height reached by the coin, in meters.

The momentum of inertia of the coin is calculated by:

(3)

Then, we expand and simplify (2):

If we know that , and , then the height reached by the coin is:

The coin will reach a vertical height of 0.027 meters before it stops rolling.

weather forecasts are done by collecting data about the current state of the atmosphere mainly the temperature, humidity and wind and using meteorology, to determine the atmosphere that evolves over time. the h and l mean the high and low pressure. the red strip is a warm front. the blue strip is a cold front. the blue and red strip is a stationary front. the purple strip is a occluded front.

explanation:

answer: (431,2)

step-by-step explanation: