A student argues that as a satellite orbits the earth in a circular path, it moves with a constant velocity and therefore has no acceleration. The professor claims that the student is wrong since the satellite must have a centripetal acceleration as it moves in its circular orbit. What is wrong with the student's argument?
The student's argument is mistaken because circular motion involves acceleration, even if the velocity remains constant. The student incorrectly assumes that any object moving with a constant velocity must have no acceleration. However, this is an oversimplification.
Acceleration is the rate of change of velocity, which includes changes in either speed or direction. In the case of circular motion, the direction of the satellite's velocity is constantly changing, even if the magnitude (or speed) of the velocity remains constant. This change in direction requires a centripetal force, which in turn produces centripetal acceleration.
Centripetal acceleration is the acceleration directed towards the center of the circular path. It is responsible for keeping an object in uniform circular motion. Without this centripetal acceleration, the satellite would no longer follow its circular orbit but would instead move in a straight line tangent to the circle.
In conclusion, the student's argument overlooks the fact that circular motion involves a change in direction, resulting in a centripetal acceleration, even if the magnitude of velocity remains constant.