Angular Speed of Earth when

[9giddjl]

Angular Speed of Earth when...

Homework Statement

Determine the angular speed with which the Earth would have to rotate on its axis so that a person on the equator would weigh 75% of their present weight (Radius of the Earth is 6400 km)

Homework Equations

wf=2pi/T
wt= mg
v=wr

The Attempt at a Solution

First I did wt=0.75 x m x 9.8, the problem is i can't find any equation that could incorporate weight and angular speed. Can somebody please give me some hints? Any help would be appreciated:) Thankyou very much

 

[mgb_phys]

Centrifugal force = m r w^2 where w is the angular speed in radians/sec.

 

[nlightner]

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I would approach this problem by first acknowledging that there is a relationship between weight, mass, and angular speed. From your attempt at a solution, it seems like you are on the right track by using the equation wt=mg, where w is the angular speed, t is the time period, m is the mass, and g is the acceleration due to gravity.

To solve for the angular speed, we need to first determine the mass of the person on the equator. We can use the equation for weight, wt=mg, and plug in the given information that the person's weight is 75% of their present weight. This would give us a new weight, let's call it w', which is 0.75 times the person's original weight. We can then set this equal to the person's mass (which remains constant) times the acceleration due to gravity (which also remains constant). This would give us the equation:

w' = m x g

Next, we can use the formula for angular speed, wf=2pi/T, where T is the time period. In this case, the time period is equal to the time it takes for the Earth to complete one full rotation on its axis, which is 24 hours or 86400 seconds. We can then plug in this value for T and solve for w, the angular speed.

w = 2pi/86400 = 7.27 x 10^-5 radians per second

This is the angular speed at which the Earth would have to rotate for a person on the equator to weigh 75% of their present weight. However, it is important to note that this is not a realistic scenario, as the Earth's rotation speed is already fixed and cannot be changed by human intervention.

In conclusion, as a scientist, I would approach this problem by using the equations for weight, mass, and angular speed, and solving for the unknown variable. I would also acknowledge any limitations or assumptions in the problem and provide a realistic explanation for the solution.