Teaching Physics with the Physics Suite Edward F. Redish Problems Sorted by Type | Problems Sorted by Subject | Problems Sorted by Chapter in UP

Eugenia in circles

 Eugenia made a video demonstrating circular motion for her physics class by going around in a circle on her rollerblades. She did this by holding on to one end of a taut rope and pushing off so she started moving perpendicular to the rope. The other end of the rope is held by her colleague, David, who is standing fixed at the center of her circle and rotating as she goes around. A picture from this video is shown at the right. After a quick start, Eugenia just has to hold onto the rope to go round in a circle at a constant speed. While she is going around her speed is v, her mass is m, the distance from David’s pivot point to the center of mass of Eugenia) is R, and the coefficient of friction with the floor is μ. Take the center of our coordinate system as David’s pivot point. (a) On the picture, draw arrows indicating Eugenia’s position vector, velocity vector, acceleration vector, and net force, labeling clearly which vector is which. (b) Find an expression for the magnitude of Eugenia’s acceleration in terms of these variables. Explain your reasoning.

(c) Find an expression for her angular velocity, ω, as a function of the given variables. Explain your reasoning.

(d) Is there a net force on Eugenia? If so, specify the kind of force and what is causing it, and how big it must be in terms of the given variables. If not, explain how you know there is none.