Chapter 11, Problem 1IP

The relative angle at the knee changes from 0° to 85° during the knee flexion phase of a squat exercise. If 10 complete squats are performed, what is the total angular distance and the total angular displacement undergone at the knee? (Provide answers in both degrees and radians.) (Answer: ϕ = 1700°, 29.7 rad; θ = 0)

Summary Introduction

To determine: The angular distance and angular displacement at the Knee.

Answer to Problem 1IP

The total angular distance for 10 squats is $1700°$, in radian $29.7\text{radian}$, and the angular displacement is zero.

Explanation of Solution

Calculation:

The angular distance knee must travel for flexion is $85°$ and similarly the angular distance for extension is also $85°$. Thus, total angular distance for one squat is $170°$.

Write the expression for angular distance.

$\text{Total}\text{angular}\text{distance}=\text{number}\text{of}\text{squats}\times \text{angular}\text{distance}\text{for}\text{one}\text{squat}$

Substitute $170°$ for angular distance for one squat and 10 for number of squats to find the total angular distance.

$\begin{array}{c}\text{Total}\text{angular}\text{distance}=\text{10}\times \text{170}°\\ =1700°\end{array}$

Therefore, total angular distance for 10 squats is $1700°$.

Convert the total angular distance for 10 squats into radian.

$\begin{array}{c}\text{Total}\text{angular}\text{distance}=1700°\left(\frac{\pi \text{radian}}{180\text{degree}}\right)\\ =29.67\text{radian}\\ \approx 29.7\text{radian}\end{array}$

Therefore, the total angular distance for 10 squats in radian is $29.7\text{radian}$.

There is no change in position after completing 10 squats, thus, angular displacement is zero.

Conclusion

Therefore, total angular distance for 10 squats is $1700°$, in radian $29.7\text{radian}$, and the angular displacement is zero.