Circular Motion: Tangential Velocity and Frequency Calculation

A. What is the magnitude of the tangential velocity of the aircraft in m/s?

If the centripetal acceleration of the aircraft is 2.00 g’s with a 200.0 m radius.

B. What is the frequency of the aircraft in rpm?

If the centripetal acceleration of the aircraft is 2.00 g’s with a 200.0 m radius.

Answer:

A. The magnitude of the tangential velocity of the aircraft is approximately 62.48 m/s.

B. The frequency of the aircraft is approximately 0.0497 rpm.

Reflecting on the calculations for the magnitude of the tangential velocity and the frequency of an aircraft moving in a circular path, we can break down the process as follows:

A. Tangential Velocity Calculation:

To determine the tangential velocity of the aircraft, we utilize the formula for centripetal acceleration, which is given as 2.00 g’s. By substituting the values into the formula v = √(2.00 * g * r), where g is the acceleration due to gravity (9.8 m/s^2) and r is the radius of the circular path (200.0 m), we find that the magnitude of the tangential velocity is approximately 62.48 m/s.

B. Frequency Calculation:

To find the frequency of the aircraft in rpm, we apply the formula f = v / (2 * π * r), where v is the tangential velocity and r is the radius of the circular path. By substituting the previously calculated tangential velocity into the formula, we arrive at a frequency of approximately 0.0497 rpm.