Why are you setting the angular velocity at 9.8? What are the units for angular velocity?thebigeis said:Suppose a space station is constructed as a 1000m-diameter cylinder that rotates about its axis. What rotation period will provide "normal" gravity?
This is the work I have for this.
angular velocity = 9.8
r = 500m
2pi500/T = 9.8
2pi500/9.8 = T
T = 320.57
What did I do wrong?
Andrew Mason said:Why are you setting the angular velocity at 9.8? What are the units for angular velocity?
What is the centripetal force as a function of rotation speed or angular velocity and radius? Set that force is equal to the force of gravity.
AM
So what is the centripetal acceleration in terms of rotational speed and radius? Set that equal to the (gravitational) acceleration you are trying to achieve. You are given the radius so you will be able to determine the angular speed needed to produce that centripetal acceleration.thebigeis said:I'm not given the angular velocity, so I'm assuming it's a number that I should already know. I don't have the mass either. Isn't "normal gravity" mass * acceleration, acceleration equaling 9.8m/s^2. This is why I'm confused. What I wrote above is all I'm given.
Andrew Mason said:So what is the centripetal acceleration in terms of rotational speed and radius? Set that equal to the (gravitational) acceleration you are trying to achieve. You are given the radius so you will be able to determine the angular speed needed to produce that centripetal acceleration.
AM
Centripetal force is the force that pulls an object towards the center of a circular path, while centrifugal force is the apparent outward force that an object experiences when it is moving in a circular motion. In reality, centrifugal force does not actually exist and is just an inertial force that arises due to the object's tendency to resist changes in its motion.
Gravity is the force that keeps objects in orbit around each other. In circular motion, gravity acts as the centripetal force, pulling the object towards the center of the circular path. Without gravity, objects would continue in a straight line and not be able to maintain a circular path.
No, circular motion cannot occur without some form of centripetal force, which can be gravity or another type of force. Without a centripetal force, objects would continue in a straight line and not be able to maintain a circular path.
The speed of an object affects its circular motion by determining how strong the centripetal force needs to be to keep the object in its circular path. The faster the object is moving, the greater the centripetal force required to maintain its circular motion.
Circular motion and angular velocity are closely related. Angular velocity is the rate at which an object rotates around a fixed point, and it is directly proportional to the object's linear speed and the radius of its circular path. In circular motion, the object's angular velocity remains constant, while its linear speed varies as it moves around the circular path.