# Work in Uniform Circular Motion

• dasrheingold

#### dasrheingold

Uniform circular motion requires a force perpendicular to the velocity. Therefore, the work done by such a force is zero because the dot product of the force and the path is zero. So there is no energy gain beyond the kinetic energy arising from its constant speed. But if I have a mass (rocket ship) traveling in a straight line in space with a constant speed, the only way I can get it to move in a uniform circle would be to have some sort of thruster acting perpendicular to the direction of movement. I am imagining a spaceship and thrusters being continually applied perpendicular to direction of motion. Energy would be depleted as the rocket fuel is used. If I stop using energy, by turning off the motor the ship stops its uniform circular motion and continues in a straight line. It seems energy must be continually expended to maintain uniform circular motion. However, this seems to contradict the accepted answer that no work is done on an object by the force that causes the uniform circular motion. What am I missing?

Turning using rockets is 100% inefficient. It uses energy for no change in energy. That is why real space missions use gravity to turn whenever possible.

Uniform circular motion requires a force perpendicular to the velocity. Therefore, the work done by such a force is zero because the dot product of the force and the path is zero. So there is no energy gain beyond the kinetic energy arising from its constant speed. But if I have a mass (rocket ship) traveling in a straight line in space with a constant speed, the only way I can get it to move in a uniform circle would be to have some sort of thruster acting perpendicular to the direction of movement. I am imagining a spaceship and thrusters being continually applied perpendicular to direction of motion. Energy would be depleted as the rocket fuel is used. If I stop using energy, by turning off the motor the ship stops its uniform circular motion and continues in a straight line. It seems energy must be continually expended to maintain uniform circular motion. However, this seems to contradict the accepted answer that no work is done on an object by the force that causes the uniform circular motion. What am I missing?

Welcome to PF dasrheingold!

You are forgetting about the mass that you have to eject outward at great speed in order to make the rocket prescribe a circle. Ejecting mass at great speed requires energy. But one does not need to continually eject mass from the system in order to create a force.

If the centripetal force is supplied by another body such that the two bodies prescribe a circle about the centre of mass of the two-body system, no mass leaves the system, no energy is expended and no work is done by either body.

AM

• PeroK
It seems energy must be continually expended to maintain uniform circular motion. However, this seems to contradict the accepted answer that no work is done on an object by the force that causes the uniform circular motion.
A hovering helicopter must continually expend energy to remain a constant altitude. Does this imply that staying at constant altitude, like a book on a table does, requires energy?