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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 t1.  Label this point as O, and draw a vector at O to represent the magnitude and direction of the object’s velocity at time t1.  Draw another dot to represent the object’s position at a later time t2, shortly after t1, and label this point P.  Draw a vector at P to show the magnitude and direction of the object’s velocity at time t2.  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 (Δv).   The change Δv is the increment that must be added to the velocity at time t1 so that the resultant velocity has the new direction after the elapsed time Δ?=?1−?2Δt=t1−t2.  Add the change in velocity Δv to your drawing of the velocity vectors; it should be a straight line connecting the heads of the vectors. Recalling the relationship between change in velocity and acceleration, construct a vector that represents the direction and magnitude of the average acceleration between the pair of velocities.  Would the direction of the acceleration be different for very close points on the object’s path? Repeat steps 1-3 for two different neighboring positions on the object’s circular path.  Is the direction of the acceleration for this pair of velocities the same, or different as before?  What can you conclude (in general) about the direction of acceleration?

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 t1.  Label this point as O, and draw a vector at O to represent the magnitude and direction of the object’s velocity at time t1.  Draw another dot to represent the object’s position at a later time t2, shortly after t1, and label this point P.  Draw a vector at P to show the magnitude and direction of the object’s velocity at time t2.  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 (Δv).   The change Δv is the increment that must be added to the velocity at time t1 so that the resultant velocity has the new direction after the elapsed time Δ?=?1−?2Δt=t1−t2.  Add the change in velocity Δv to your drawing of the velocity vectors; it should be a straight line connecting the heads of the vectors. Recalling the relationship between change in velocity and acceleration, construct a vector that represents the direction and magnitude of the average acceleration between the pair of velocities.  Would the direction of the acceleration be different for very close points on the object’s path? Repeat steps 1-3 for two different neighboring positions on the object’s circular path.  Is the direction of the acceleration for this pair of velocities the same, or different as before?  What can you conclude (in general) about the direction of acceleration?

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  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 t1.  Label this point as O, and draw a vector at O to represent the magnitude and direction of the object’s velocity at time t1.  Draw another dot to represent the object’s position at a later time t2, shortly after t1, and label this point P.  Draw a vector at P to show the magnitude and direction of the object’s velocity at time t2. 
  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 (Δv).   The change Δv is the increment that must be added to the velocity at time t1 so that the resultant velocity has the new direction after the elapsed time Δ?=?1−?2Δt=t1−t2.  Add the change in velocity Δv to your drawing of the velocity vectors; it should be a straight line connecting the heads of the vectors.
  3. Recalling the relationship between change in velocity and acceleration, construct a vector that represents the direction and magnitude of the average acceleration between the pair of velocities.  Would the direction of the acceleration be different for very close points on the object’s path?
  4. Repeat steps 1-3 for two different neighboring positions on the object’s circular path.  Is the direction of the acceleration for this pair of velocities the same, or different as before?  What can you conclude (in general) about the direction of acceleration?
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