Roth+Lab+15

Lab 15 Physlets Illustration 10.1

The component form of the point on a circle consists of the x and y coordinates. The vector form of a point on a circle demonstrates the magnitude of the vector, which is the radius, and the angle that vector makes with the positive x-axis. The magnitude of the vector is constant in a circular motion since the magnitude is the radius, and the radius has to be constant in order for it to be a circle. There is a relationship between the radius, the angle in radians of the vector, and the arc length. Theta= s/r or s=r(theta) Since the arc is the linear distance traveled, s=vt can be used when the motion is uniform. Therefore, if you substitute vt for s, the equation can be rewritten as: Theta=(vt)/r, and v/r is the angular velocity, omega, so the equation can again be rewritten: Theta= omega x t When there is a constant angular acceleration, called alpha, it is related to the tangential acceleration by at/r.