Question

A golf club driver is swung and hits a golf ball. The driver has a shaft of length L and a head. To simplify the problem, we will neglect the mass of the driver shaft entirely. The driver head we will assume is a uniform density sphere of radius R and mass M. The golf ball is a uniform density sphere of radius r and mass  m. Initially the ball is at rest, with zero linear velocity, v → 2 i = 〈 0 , 0 , 0 〉, and zero angular velocity, ω → 2 i = 〈 0 , 0 , 0 〉. The driver head has an initial linear velocity of v → 1 i = v 1 i 〈 1 , 0 , 0 〉. Immediately after the collision the golf ball has linear velocity v → 2 f = v 2 f 〈 cos ⁡ θ , sin ⁡ θ , 0 〉and angular velocity ω → 2 f = ω 2 f 〈 0 , 0 , 1 〉. This angular velocity of the golf ball is commonly referred to as "backspin". Recall that the moment of inertia for a sphere rotating about its center of mass is I = 2 M R 2 5.

You can assume that the parameters described in the previous paragraph are the known quantities in the problem. In the questions that follow, you can write your results in terms of these known values: L , M , R , m , r , θ , v 1 i , v 2 f , ω 2 f.  

Consider the system of the golf club plus the golf ball. For the short duration of the collision, we can neglect any external forces on the system (the force exerted on the club by the golfer's hand would be an example). In this case, the linear momentum of the system (driver + ball) is conserved. Use this information to determine the final velocity of the driver head, v → 1 f. Express your result as a three-component vector.  

Answer 1