Question

Bio-mechanics: Use an equation and concept of linear and angular kinematics to explain why the driver (club used to hit the ball the farthest in golf) is the longest club used in golf.

Answer 1

on To begin analysis lets look at the strobe picture of Bobby The red cree braces the notion of his hands at the .. grip location throughout the swing . The blue were traces the motion of the club head throughout the swing The red come is almost a perfect circle , as you can see in The blue wree i not a circle but is. spiral shaped The largest radius of the blue corre occurs at the bottom of the swing where the dub is fully exterded We draw a schematee of the set up a The physes behind the swing will be treated here as a two denunsional problem Terd-90 Q14 DIA arm r x Ground هيل where, r = Radies of the golfer's swing where P = Grup location where the golfer is holding on to the b = certre of mass of the golf cob 'S = Distance from p to the center of mass of the goy deb o = Swing angle the golferi angle avem make with the vertical

az apple the golf club makes with the golferie arme Next, we need to draw a free-body diagram of the goll dob This is the important object of study since it in the golf club that is reaiting to usput from the golfer, so it must be isolated from the system. Gluy) ota-ao - - - - - - Me where g = 9.8 m/s² lehub = length of the club m = Moment of nertia exerted on the golf club at p by the players hands. fen - Horizontal force exerted on the golf club ate by the players hands. feo = vertical force enerted on the golf club at P by the I playwis hands and Glny) = position in cortesian wordenates of the center of mass to We can express the position of the centre of mass as follows x = -r Suo + 4 cos (o+x-90) kent x = -resco + la seu Cora)

goy - y = 1080 + 4 Silora-90) y = ruso - Locos (ota) Newtons and law we write the a-due general force a Using in the E = maga where Efn = sum of the forces is the x-dix m = mass of the golf clube aan = Acceleration of the center of the mass the x-den, want ground! in Note that Thus we have e fpe & m {re sino (0) - 46 Su (Ota). (6 tà) + 6 ces (94 m). } -0 for simplicity de=0 c da dt daa ç C for simplicity, it is also assumed that the golfere arme robale at a constant angular wel. On other worde, the angular acceleration is zero.

This -o the genered force of is up Sunilary by Necoton's and how the y-der is Etymo ay The colere mass in the Ify = Sum of forces in the y-dii Gy= Acceleration of the centre of g-dea wrot ground. This Note that part pt This we have for my = mf-recoso. (0) + li ces (Ora) (0 tar + 6 sn (Oto). ä J - tale must now write the general moment en for rotation of a regend body about its center of Arges mais be . Ma - Zaldub . where EMo = Sum of moments about the center of mass IG= Moment of inentin of the golf club about its center of mass , about an anis pourting out of the page I doo = Anguber all of the club! Note that tot a club - o ta This is the angular acceleration of the golf club wort ground.

2. - Thus, the moment of an becomes mp - for a la cas 10ta) - fai la Sin 10ta) - Inä - To solve these and we can substitute o s W isto o 7 The resulting of is as follows : - "Sino (6) m la us @ + x) - mg la Su Cota) + acoso (6) mla &is (eta) = (lam+76) 2 This is a and order differential e q is terns of a . It can only be solved nonvinally . It will solved for the part of the swing where the wrists are uncocked ,& subject to the following initial conditions at the release of .pt, giver as x=90 x = 0 Note that a =900 is a common angle that golfers hold the club relative to their arms , prior to uncocking their wrists An additional condition is that Mp =0 since the corests are allowed to rotate freely at the release pt, s every pt is the swing thereafter The other unknown quantities is the equation such as a mi Io are constants based on the properties of the golf clob & the parameters of the golfere swing. out