- #1
lemon
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Homework Statement
Ignoring the motion of the Earth around the Sun and the motion of the Sun through space, find:
a) the angular velocity
b) the linear speed
c) the centripetal acceleration
of a body resting on the ground at the equator.
What would the length of a day be if the angular speed of the Earth's rotation on its axis were to increase until the body became effectively weightless? Radius of Earth = 6.4 x 106m
Homework Equations
1: ω=θ/t
2: v=2πr/T and v=ωr
3: a=v2/r and a=rω²
The Attempt at a Solution
a) ω=θ/t
Hmmm!
We have 24 hours for one complete rotation of the Earth = 24x60x60=86400s
One complete rotation = 360° = 2π(rads)
Therefore, 2π/86400s=73x10-6rad s-1 (2s.f.)
b) v=ωr
v=(73x10-6)x(6.4x106)=467.2m/s
c) a=rω2
a=(6.4x106)x(73x10-6)2=0.0341056m s-1
=34.1x10-3m s-1
In order to answer the last part of the question, I guess we must consider what angular speed would cause the body to become effectively weightless. We don't have a mass of the body (kg) and therefore, can't calculate its weight.
I'm lost. Please advise and check first part of question.
Much appreciated as always