Question

through how many radians does a point on the earth's surface move in 6.00h as a result of the earth's rotation? what is the speed of a point on the equator? take the radius of the earth to be 6370km
​

Answer 1

Answer:

Given Data:

The time in which the point moves is:

T=6h

The radius of the earth is:

R=6370 km

The time required by the earth to complete one rotation is:

t=24h

The expression for the distance covered by the point on the earth's surface is,

θ=ωT⋯⋯(1)

The expression for the angular speed of the earth is,

ω=2πt⋯⋯(2)

Here, the time required to complete one rotation is

t.

Substitute Equation (2) in Equation (1).

θ=(2π t)T

Substitute the values in above expression.

θ=(2π24h) (6h) θ=1.571rad/s

Thus, the distance covered by the point on the earth's surface is

1.571

rad/s.

The expression for the linear velocity of the point on the equator is,

V=Rω

Substitute the values of \omega in above expression.

V=R(2πt)

Substitute the values in above expression.

V=(6370km)(2π24hV=6370km)

(2π24×60×60sV=(0.463239kms(1000m1km)V=463.29s

Thus the linear velocity of the point on the equator is

463.239m/s.