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Chapter 4: Problem 111

The angular velocity of a point on Earth is \(\frac{\pi}{12}\) radian per hour. Describe what happens every 24 hours.

Short Answer

Expert verified
A point on Earth completes a full rotation or 360 degrees in a 24-hour period.

Step by step solution

01

Identify the meaning of angular velocity

The angular velocity given represents the rotational speed of Earth. The unit, radian per hour, indicates that it describes how many radians the Earth rotates per hour.
02

Rationalize the time frame

We have to understand what happens in a 24-hour period. This period, in terms of hours, is the time for which we want to calculate the total rotation.
03

Calculate total rotation

To find out the total angle turned by the Earth in 24 hours, multiply the angular velocity \(\frac{\pi}{12}\) by the number of hours in a day (24 hours). The result is \(\frac{\pi}{12} * 24 = 2\pi\) radians.
04

Interpret results

Point on Earth completes a full rotation in 24 hours. The value \(2\pi\) radians equals 360 degrees, which corresponds to a full rotation.

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