FORMULAS AND INFORMATION TO USE: - 360 degrees = 2pi radian or 6.284 - 1 radian = 360 degrees / 6.284 - 1 radian =57.3 degrees -(x) angle in degrees/57.3 degrees radian = (x) radians -(x) radians * 57.3 degrees/ radians = (x) degrees - Absolute [segment] angles: theta = tan^-1 (opp/adj) = y2-y1/x2-x1 = proximal y distal y divided by proximal x - distal ✗ - If a negative angle is clockwise from the left horizontal, to convert counter-clockwise angle from the right, add 180 degrees. oppy2-Y1 adi = X2-X1 (X2,Y2) opp Ꮎ (X1.V1) adj - To calculate relative angles, use the formulas: Ohip = thigh-trunk Oknee = Othigh- Oshank Oankle = foot-shank - 90° tane shank Kneey Ankley Kneex Anklex - Angular velocity is also απ Δω Δι i At - Angular acceleration (a) = wfinal-winital (units is Tad tfinal-tinital • Angle ([A]in radians) = • Arc length (As) Radius of rotation (r) Arc length(As) = Radius of rotation(r) x angle ([A]in radians) • LINEAR AND ANGULAR DISPLACEMENTS As = r AO • Tangential velocity formula is ✓=r*w (answer should be in m/s) * AO, THETA, R, A AND or w (OMEGA) need to be converted to radians. AS1 * Linear velocity = At Τ1 Αθ At • Tangential (VT) velocity depends on . Distance from radius of rotation (r) Angular velocity (w) EXAMPLLE OF TANGENTIAL VELOCITY WITH A FOOT: foot tangential velocity (VTfoot) depends on thigh Whip Wknee shank wwww Change in position ⚫Thigh length (high) and hip angular velocity (whip) •Shank length (shank) and knee angular velocity (knee) • Vr foot = ("thigh x Whip) + (Tshank xwknee) • To increase the foot tangential velocity, increase angular velocity of thigh and shank rotation Vfoot - Angular displacement is (A0) = RADIANS.) Ofinal Oinitial (NEVER EXCEEDS 360 DEGREES OR 2 PI Initial position Final position - Angular speed = angular distance/time (units is rad/s). - Angular velocity (w) final - initial = (units is rad/s) time final - time initial Hip (1.32, 0.75) Knee (1.62, 0.51) Thigh 0Knee. Ꮎ . Shank Calculate the following: Ankle (1.35, 0.23) a. Thigh segment angle (0 Thigh) Draw a diagram here. Write the equations and show all your work. b. Shank segment angle (leg) Draw a diagram here. Write the equations and show all your work. c. Knee joint angle (knee) Draw a diagram here. Write the equations and show all your work.

Sagittal plane hip, knee, and ankle coordinates were digitized (shown in the figure) from the right lower extremity of a person walking. Provide the equations, show all the steps, and provide correct units with the answers. Provide answer to 2 decimal places unless stated otherwise. USE ONLY the formulas provided please! PLEASE ALSO DON'T FORGET TO DRAW ALL DIAGRAMS. Answer parts a-c.