Final answer:
The angular speed of Earth is approximately 0.0000727 radians per second. Arlington's linear speed and centripetal acceleration can be calculated using its latitude and Earth's radius. The ratio of Arlington's linear speed to that at the equator is determined by the cosine of Arlington's latitude.
Step-by-step explanation:
Angular Speed of the Earth
The angular speed of the Earth is constant and can be calculated using the formula ω = 2π / T, where T is the period of Earth's rotation, which is approximately 24 hours or 86400 seconds. Therefore, the angular speed ω is roughly 0.0000727 radians per second.
Linear Speed and Acceleration at Arlington
The linear speed v of Arlington can be found by v = ω × R × cos(λ), where R is the Earth's radius (approximately 6371 km) and λ is the latitude of Arlington. Given as 32.7357°, this would result in a specific linear speed for Arlington. Acceleration a is given by a = v² / R. This would give the centripetal acceleration for Arlington due to Earth's rotation.
Ratio of Linear Speeds
The linear speed of a point at the equator is the maximum linear speed due to rotation, which can be calculated by simply using v = ω × R, ignoring the cosine factor since the latitude at the equator is 0°. The ratio of Arlington's speed to that of the equator's can thus be found by dividing Arlington's linear speed by the equator's linear speed.