Question

need help on numbers 4-6

1. Make a drawing of the path of an object in circular motion at constant speed. On that path, use a dot to represent the object’s position at time t 1 . Label this point as O, and draw a vector at O to represent the magnitude and direction of the object’s velocity at time t 1 . Draw another dot to represent the object’s position at a later time t 2 , shortly after t 1 , and label this point P. Draw a vector at P to show the magnitude and direction of the object’s velocity at time t 2 .

2. Redraw the velocity vectors with the tail of one vector (point P) at the tail of the other vector (point O). Keep the same size and direction as in the previous drawing. To find the acceleration of the object, you are interested in the change in velocity ( v). The change v is the increment that must be added to the velocity at time t 1 so that the resultant velocity has the new direction after the elapsed time t=t 2 – t 1 . Add the change in velocity v to your drawing of the velocity vectors; it should be a straight line connecting the heads of the vectors.

3. On your drawing from question 1, label the distance r from the center of the circle to points O and P. In the limit that the time interval is very small, the arc length distance traveled by the object can be approximated as a straight line. Use this approximation to label the CIRCULAR MOTION AND ACCELERATION (PART A) distance traveled by the object along the circle from point O to P in terms of the object’s velocity and the elapsed time.

4. The triangle drawn in question 2 (with v and Δv) is similar to the triangle drawn in question 3 (with r and the straight line distance traveled by the object) because they have the same apex angle. Use the relationship of similar triangles to write an equation that connects the sides and the bases of the two triangles.

5. Solve your equation for Δv/Δt to get an expression for the acceleration in terms of the object’s uniform velocity and the distance r.

6. From your equation, is the acceleration of an object in circular motion ever zero? Does the magnitude of the acceleration change with time?

Answer 1