High School

Estimate what Earth's rotational acceleration would be in [tex]\text{rad/s}^2[/tex] if the length of a day increased from 24 hours to 48 hours during the next 100 years.

Answer :

The orbital speed is [tex]7.272\times10^{-5}[/tex].

We need to calculate the initial and final angular speed.

The distance the body travels in relation to the number of rotations or revolutions per unit of time is determined using the angular speed formula.

The speed of an object determines how swiftly or slowly it moves. The orbital speed of an item in rotation is known as its angular speed.

[tex]w_{o}=\frac{2\pi}{t}=\frac{2\pi}{24\times60\times60}=7.272\times10^{-5[/tex]

The final angular speed is

[tex]w_{f} =2w_{o}[/tex]

So, the angular acceleration is,

Angular acceleration is the term used to describe the temporal pace at which angular velocity varies.

[tex]\alpha=\frac{w_{f} -w_{o} }{t}=\frac{w_{o} }{t}[/tex]

On solving we get,

[tex]\alpha=2.306\times10^{-14} \frac{rad}{s^2}[/tex]

Learn more about orbital speed

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