Chapter 10, Problem 15A

Three locations on our rotating world are shown. Rank these locations from greatest to least for the following quantities.

a. rotational speed about Earth’s polar axis

b. tangential speed

To determine

To rank:The locations from greatest to least based on the given quantity.

Answer to Problem 15A

The rank of places based on the rotational speed about Earth’s polar axis from greatest to least is $\text{A}=\text{B}=\text{C}$ .

Explanation of Solution

Given:

The three locations are shown below.

  

Formula used:

The rotational speed is the number of rotations per unit of time. It is expressed as revolutions per minute (RPM).

The expression for rotational speed is

  $\omega =\frac{2\pi }{T}$

Here, $T$ is the time period.

Calculation:

The rotational speed of the Earth about its polar axis is same for all the locations.

All the three locations A, B, and C rotate about Earth’s polar axis in the same amount of time.

So the three locations A, B, and C have the same number of rotations.

Conclusion:

Thus, the rank of locations on the basis of rotational speed about Earth’s polar axis from greatest to least is $\text{A}=\text{B}=\text{C}$ .

To determine

To rank:The locations from greatest to least based on the given quantity.

Answer to Problem 15A

The rank of the tangential speed from greatest to least is $\text{C}>\text{B}>\text{A}$ .

Explanation of Solution

Given:

The three locations are shown below.

  

Formula used:

The speed of an object moving along a circular path is known as tangential speed. The direction of motion for the tangential speed is always tangent to the circle.

The expression for tangential speed is,

  $v=r\omega$

Here, $r$ is the radial distance and $\omega$ is the rotational speed.

Calculation:

The rotational speed of the three locations A, B, and C have the same number of rotations.

Hence, the tangential speed is varies in direct proportion to the radial distance of the location from the rotational axis.

The radial distance of location A is nearer to the rotational axis when compared to the locations B and C.

The radial distance of location C is farther away from the rotational axis when compared to the locations A and C.

Hence, the rank of the tangential speed from greatest to least is $\text{C}>\text{B}>\text{A}$ .

Conclusion:

Thus, the rank of the tangential speed from greatest to least is $\text{C}>\text{B}>\text{A}$ .