the arc from point a to the north pole of a planet subtends a central angle of 45°, as shown in the figure…

the arc from point a to the north pole of a planet subtends a central angle of 45°, as shown in the figure to the right. the radius of the planet is 4250 mi. any point on the surface of the planet (except at the poles) makes one revolution (2π radians) about the axis of the planet in 20 hours. what are the angular and linear velocities for point a with respect to its rotation around the axis of the planet? the angular velocity is radians per hour. (simplify your answer. type an exact answer, using π as needed. use integers or fractions for any numbers in the expression.)

the arc from point a to the north pole of a planet subtends a central angle of 45°, as shown in the figure to the right. the radius of the planet is 4250 mi. any point on the surface of the planet (except at the poles) makes one revolution (2π radians) about the axis of the planet in 20 hours. what are the angular and linear velocities for point a with respect to its rotation around the axis of the planet? the angular velocity is radians per hour. (simplify your answer. type an exact answer, using π as needed. use integers or fractions for any numbers in the expression.)

Answer

Explanation:

Step1: Recall the formula for angular velocity

Angular velocity (\omega=\frac{\theta}{t}), where (\theta) is the angle of rotation and (t) is the time taken.

Step2: Identify the values of (\theta) and (t)

Given that any point (except poles) makes one revolution ((\theta = 2\pi) radians) in (t = 20) hours.

Step3: Calculate the angular velocity

Substitute (\theta = 2\pi) and (t = 20) into the formula (\omega=\frac{\theta}{t}). So, (\omega=\frac{2\pi}{20}=\frac{\pi}{10}) radians per hour.

Answer:

(\frac{\pi}{10})