Solve Tangential Speed Equation: Planet Radius 5.99x10^6 m, G-Accel 7.87 m/s^2

In summary, the question asks what the tangential speed would be for a person standing at the equator of a planet with a radius of 5.99x10^6 m and free-fall acceleration of 7.87 m/s^2. The formula for tangential velocity is Vt=rW and the formula for centripetal acceleration is ac=Vt^2/r. By setting the gravitational acceleration and centripetal acceleration equal, the person at the equator would be moving at a high speed.
  • #1
Ripcurl
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Homework Statement



If the rotation of a planet of radius 5.99x10^6 m and free-fall acceleration 7.87 m/s^2 increased to the point that the centripetal acceleration was equal to the gravitational acceleration at the equator, what would be the tangential speed of a person standing at the equator?


Homework Equations


Vt=rW (tangential velocity equals radius times omega, or angular velocity)


The Attempt at a Solution


I don't even know how to go about solving this. The way the problem is set up is confusing to me. This is the only problem out 30 some-odd questions that I have not done correctly. My homework is due at 12:00 tonight and I have almost an A, but this question is really bothering me. Can someone help?
 
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  • #2
I hope you're not on Eastern Standard Time. You are given the gravitational acceleration. What's the formula for centripetal acceleration? Set them equal.. you'll be going real fast...
 

1. What is the formula for tangential speed?

The formula for tangential speed is v = √(GM/r), where v is the tangential speed, G is the universal gravitational constant, M is the mass of the planet, and r is the distance from the center of the planet.

2. How do I calculate tangential speed if I have a planet's radius and gravitational acceleration?

To calculate tangential speed using the given information, plug the values into the formula v = √(GM/r). Remember to convert the radius to meters and the gravitational acceleration to meters per second squared.

3. What is the planet's tangential speed if its radius is 5.99x10^6 m and the gravitational acceleration is 7.87 m/s^2?

Using the formula v = √(GM/r), we can calculate the tangential speed by plugging in the given values: v = √((6.67x10^-11 Nm^2/kg^2)(5.99x10^24 kg)/(5.99x10^6 m)). This gives us a tangential speed of 7.66x10^3 m/s.

4. How does changing the planet's radius affect its tangential speed?

Increasing the planet's radius will decrease its tangential speed, while decreasing the radius will increase the tangential speed. This is because tangential speed is inversely proportional to the radius in the tangential speed equation.

5. Can the tangential speed of a planet ever be greater than the speed of light?

No, according to the laws of physics, the speed of light is the maximum speed that anything in the universe can travel. Therefore, the tangential speed of a planet can never exceed the speed of light.

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