Lab 5:  Angular Kinematics-Angular to Linear Conversions

Purpose:

To learn how to calculate angular displacement, angular velocity, and angular acceleration. In addition, you will learn about the equations for converting angular displacement to linear displacement and angular velocity to linear velocity.

Videotaping:

Step 1: One person should stand with their throwing arm side facing the video camera. Adjust the video camera by zooming in or out until you can see the upper body and arm throughout the underhand throwing motion. You should zoom in or out to make the picture as large as possible while still being able to see the arm throughout the throwing motion.

Step 2: Once you have adjusted the zoom on the camera do not change it. Videotape a meter stick for 5-10 seconds.

Step 3: Videotape the ball being thrown. Videotape the activity using the three different settings for shutter speeds (1/250 sec, 1/500 sec, 1/1000 sec).

Calculations:

Step 1: Using the VCR and TV tape a transparency to the television screen. With permanent markers, mark both ends of the meter stick that was recorded earlier.

Step 2: View the ball throws and choose the screen where the arm is the least blurry. (Most likely a darker screen and faster shutter speed.)

Step 3: Push the jog/shuttle button on the remote control. Use the outside edge of the jog/shuttle dial to fast forward the videotape until the ball is three frames past its release point. Work backwards from this to prevent fuzziness at the top of the screen.

Step 4: Place your finger in the indented circle on the jog/shuttle dial and go backwards (counter-clockwise) marking the hip joint, shoulder joint, elbow joint, wrist joint and the ball after every click or frame (one click equals one frame). Continue marking the hip joint, shoulder joint, elbow joint, wrist joint and the ball every frame until the top of the throwing motion. Use a different color marker for each frame. Mark the frame where the ball was released with an *.

Step 5: Remove transparency and gather a ruler, protractor, scientific calculator, and pencil to fill in the table with results. First, measure the distance between the ends of the meter stick marks in millimeters. You will use this measurement to determine the appropriate scale. (The meter stick will be necessary for the linear components only. The meter stick is not needed to calculate the angular components.)

Step 6: Measure the distance between each ball in millimeters and convert the measurement into meters using the calculation below. This is your displacement.

Distance between balls (mm) = distance between balls (m)/meter stick measurement (mm)

Step 7: Connect the dots that represent the hip joint, shoulder joint, elbow joint and wrist joint using a ruler and permanent marker. This will create a stick figure for each frame.

Step 8: Measure the shoulder and elbow joint angles for each frame.

Step 9: The video camera records 60 frames per second or one frame each 0.0167 seconds. Using the angular displacement (degrees) and the time (seconds) calculate the angular velocity and angular acceleration of the shoulder and elbow joints for each frame.

Displacement q = <2-<1

Velocity w = q/Dt

Acceleration a= w2-w1/Dt

Step 10: Calculate the linear displacement and linear velocity of the ball.

Step 11: On your transparency connect the dots representing the shoulder and ball for the frame just prior to ball release and the frame at release. Calculate the angular displacement and angular velocity for the shoulder/ball lines.

Step 12: Using the following equations convert the angular displacement and angular velocity values found in Step 11 to linear displacement and linear velocity.

d = rq
v = rw

Questions:

  1. Graph the angular velocity of the shoulder.  What pattern does the angular velocity of the shoulder follow?

    2.   
     
     
  2. Graph the angular velocity fo the elbow.  What pattern does the angular velocity of the elbow follow?

    3.   
     
     
  3. Where is the angular velocity of the shoulder greatest?

    4.  
     
     
  4. Where is the angular velocity of the elbow greatest?

    5.  
     
     
  5. How does your angular displacement and angular acceleration differ from what you expected?

    6.  
     
     
  6. What are some possible explanations for the error between what you expected and what you observed?

    7.   
     
     
  7. How well did your angular to linear conversion values compare to your actual linear values?

    8.  
Shoulder
Frame # Dt=t2-t1 Absolute angle q = <2-<1 w = q/Dt a= w2-w1/Dt
Change in time Angle (o) Angular Displacement (o) Angular Velocity
(o/s)		 Angular Acceleration (o/s2)
         
         
         
         
         
         
         
         
         
         

Elbow
  Dt=t2-t1 Absolute angle q = <2-<1 w = q/Dt a= w2-w1/Dt
Frame # Change in time Angle (o) Angular Displacement (o) Angular Velocity
(o/s)		 Angular Acceleration (o/s2)
           
           
           
           
           
           
           
           
           
           
           

Ball
  Dt = t2-t1 d = p2-p1 convert to meters v = d//Dt a = v2-v1/Dt
Frame # Change in time displacement (mm) displacement (m) Resultant Velocity Resultant Acceleration
           
           
           
           
           
           
           
           
           
           
           
           
           
           
           

Linear displacement of ball at release:

Linear velocity of ball at release:

Angular displacement of shoulder/ball at release:

Angular velocity of shoulder/ball at release:

Angular displacement to linear displacement conversion for shoulder ball d = rq:

Angular velocity to linear velocity conversion for shoulder ball v = rw: