Centripetal Acceleration and Static Friction: "Ladybug Revolution" Record this value of the angular velocity in the table below. Repeat this for R = 2 m, and R = 3 m. Introduction: When an object undergoes circular motion, the object acquires an acceleration directed toward the center of that circle even when its speed is constant. This acceleration is called the centripetal acceleration and is related to the object's speed by D'O a = R where v is the object's speed and R is its distance from the center of the circle; the direction of this acceleration is from where the object is located at a particular instant to the center of the circle. As we know from Newton's second law, a force must have caused this acceleration. This force can be the normal force (e.g. the force a seat exerts on a passenger in a Ferris wheel) and it can be the force of static friction (e.g. a ladybug sitting on a spinning turntable). We write Newton's second law for such an object: F = ma = m- R We consider the case of a ladybug standing on a rotating turntable; the force involved is that of static friction, we can write: F = f, = u,N. Since there is no motion in the vertical direction, it follows, then, N = mg. Putting all this into Newton's second law, we can write @ (rad/s) V = OR (m/'s) usmg = m- R R = 1 m R = 2m Cancelling the mass, we obtain R= 3m Average . = Ng = Now, place the bug at the edge (be sure when the table rotates the bug rotates with it). Procedure: Click on the following link and download "Ladybug Revolution". In this case R = 4 m. Using the average / you calculated earlier, calculate the angular velocity needed to get the bug off the table. Show your calculation. https://phet.colorado.edu/en/simulation/legacy/rotation Verify this prediction with the simulation and comment on how well your calculation agreed with the simulation. Once you open the simulation, click on the "Rotation" tab. You should see a setup similar to that shown below. Place one of the bugs at a distance 1 meter away from the center. Note that each bug has a dot on its back; be sure that this dot matches with the 1 meter mark. In the angular velocity box, input 5 and press "Go!" The turntable should start spinning at an angular velocity @ = 5 rad/s. Next, enter 10 for the angular velocity, now the bug will spin even faster. Keep increasing the value of the angular velocity until the bug falls off the table. Be sure you get the angular velocity at which the bug falls off the table to an accuracy of 0.5 rad/'s