How Do You Calculate Angular Distance and Displacement in Biomechanics?

[nsxviper]

Homework Statement

A tennis player takes 3 preparatory swings, each swing travels through an arc of 140 degrees each way. At the 4th swing, the ball is struck and the swing travels 240 degrees. Calculate the total angular distance and angular displacement of the club.

Homework Equations

I have no clue, is it theta = d/r ?

The Attempt at a Solution

I am so confused because all I am given is the arc and no radius. Is the angular distance in rads or meters? I can't seem to find the formula for this. I've taken physics and I know how to solve for angular velocity and angular acceleration but never did solve for angular distance. This is for my biomechanics class.

 

[tiny-tim]

Welcome to PF!

Hi nsxviper! Welcome to PF!

… I've taken physics and I know how to solve for angular velocity and angular acceleration but never did solve for angular distance.

Since you obviously understand the difference between angular velocity and ordinary velocity, and between angular acceleration and ordinary acceleration, just go with the flow … the difference between angular distance and ordinary distance is exactly the same.

a (tangential) = rα

v (tangential) = rω

s (tangential) = rθ

(and so, for example, if you've done the standard constant acceleration equations, v = u + at etc, you can apply them to constant angular acceleration, just substituting α for a, ω for v, and θ for s)

 

[kerimek]

I can provide a response to this content by first clarifying that angular distance is measured in radians, not meters. The formula for angular distance is indeed theta = d/r, where d is the arc length and r is the radius. In this case, since the arc length and radius are not given, we cannot calculate the exact value of the angular distance. However, we can still calculate the total angular distance and angular displacement of the club by using the given information.

To find the total angular distance, we can add up the angular distances of each swing. In this case, the first three swings each travel through an arc of 140 degrees, so the total angular distance would be 140 + 140 + 140 = 420 degrees. This is equivalent to 7π/3 radians.

To find the angular displacement, we need to calculate the difference between the final position of the club and its initial position. In this case, the club starts at 0 degrees and ends at 240 degrees, so the angular displacement would be 240 - 0 = 240 degrees. This is equivalent to 4π/3 radians.

In summary, the total angular distance of the club is 420 degrees or 7π/3 radians, and the angular displacement is 240 degrees or 4π/3 radians. It is important to note that the units for angular distance and angular displacement are in radians, not degrees.