What is the linear speed of a point (a) on the equator, (b) on thearctic circle (latitude 66.5o n), and (c) at a latitudeof 45.0 degrees n, due to the earth's rotation?
for part (a), i used the equation w = a/t to represent that theearth rotates once a day on its axis. a point on the equatorthus rotates through 2πradians in 24 hours, so
w = a/t = (2π) / (24 hr) = (6.28 rad) / (24hr x 3600 s/hr) = 7.27 x 10-5 rad/s
since the radian is a unitless measure it is not necessary toinclude it in the units for a quantity.
the radius of the earth is re = 6.4 x 106 m, so:
v = wr = (7.27 x 10-5 rad/s)(6.4 x106 m) = 465 m/s = 1674 km/hr

a)   v = 465.3 m / s , b)     v = 196.3 m / s , c)  v =327.2 m/s

Explanation:

Linear and angular magnitudes are related.

               v = w r

Where v and w are the linear and angular velocities, respectively and r is the radius of the circle.

Let's look for angular velocity

In rotated angle is a rotation of the Earth is 2π rad and the Time spent Period is24 h

Let's reduce the hours to seconds

       T = 24 h (3600 s / 1 h) = 86,400  s

       w = 2π / 68400

       w = 7.27 10⁻⁵ rad / s

Let's look for linear speeds

a) in Ecuador the radius of the circle is the radius of the planet

      r =   = 6.4 10⁶ m

      v = 7.27 10⁻⁵ 6.4 10⁶

      v = 465.3 m / s

b) As the sphere reduces the size of the circle, let's use trigonometry to find the triangle leg, the angle is measured from the x-axis (East

       cos 65 = r /  

       r = cos 65

       r = 6.4 10⁶ cos 65

       r = 2.7 10⁶ m

  We calculate the linear speed

       v = 7.27 10⁻⁵ 2.7 10⁶

       v = 196.3 m / s

c) at an angle of 45

        r = 6.4 10⁶ cos45

        r = 4.5 10⁶ m

        v = 7.27 10⁻⁵ 4.5 10⁶

        v =327.2 m/s

a high pressure system is a dense air mass that is usually cooler and drier than the surrounding air. a low pressure system is a less dense air mass that is usually wetter and warmer than the surrounding air.

in general, areas that experience high atmospheric pressure also experience fair weather. low pressure systems can cause the formation of clouds and storms. air usually flows from areas of high pressure to areas of low pressure..

heats surface water up