Calculating Angular and Radial Acceleration in Circular Motion

[SUchica10]

What are (a) the angular speed, (b) the radial acceleration, and (c) the tangential acceleration of a spaceship negotiating a circular turn of radius 3220 km at a constant speed of 28,700 km/h?


I am not sure what formulas to use... any suggestions would be appreciated.

 

[Pyrrhus]

This is straightforward, check your textbook.

 

[kyle8921]

(a) The angular speed, or angular velocity, of the spaceship can be calculated using the formula ω = v/r, where v is the linear speed and r is the radius of the circular turn. In this case, the angular speed would be ω = (28,700 km/h) / (3220 km) = 8.92 radians/hour.

(b) The radial acceleration, or centripetal acceleration, of the spaceship can be calculated using the formula a = v^2/r, where v is the linear speed and r is the radius of the circular turn. In this case, the radial acceleration would be a = (28,700 km/h)^2 / (3220 km) = 256,085.7 km/h^2.

(c) The tangential acceleration of the spaceship can be calculated using the formula a = ω^2r, where ω is the angular speed and r is the radius of the circular turn. In this case, the tangential acceleration would be a = (8.92 radians/hour)^2 (3220 km) = 102,543.2 km/h^2.