During a biceps curl, the elbow's relative angle during flexion changes from 3° to 157°. During an 8 repetition set, what is the total angular distance and displacement at the elbow in degrees and radians?
1600
To find the total angular distance at the elbow during a set of biceps curls, we need to calculate the difference between the initial and final angles for each repetition and then sum them up. Similarly, the total angular displacement is the absolute value of the difference between the initial and final angles, regardless of the direction.
Let's calculate the angular distance first:
1. Find the difference in angles for each repetition:
- 1st repetition: Final angle – Initial angle = 157° - 3° = 154°
- 2nd repetition: Final angle – Initial angle = 157° - 3° = 154°
- 3rd repetition: Final angle – Initial angle = 157° - 3° = 154°
... and so on until the 8th repetition.
2. Sum up the angular differences for each repetition:
Total angular distance = 154° + 154° + 154° + ... (eight times)
To calculate the total angular displacement, we need to take the absolute value of the difference in angles for each repetition:
1. Find the absolute difference in angles for each repetition:
- 1st repetition: |Final angle - Initial angle| = |157° - 3°| = 154°
- 2nd repetition: |157° - 3°| = 154°
- 3rd repetition: |157° - 3°| = 154°
... and so on until the 8th repetition.
2. Sum up the absolute angular differences for each repetition:
Total angular displacement = 154° + 154° + 154° + ... (eight times)
To convert the total angular distance and displacement to radians, we can use the conversion factor:
1 radian = 180° / π
Multiply the total angular distance and displacement in degrees by π/180 to get the values in radians.
Note: In this example, I assumed that each repetition starts from the same initial angle of 3° and ends at the same final angle of 157°. In reality, there could be variations between repetitions, but this is the basic calculation method.