Question

Consider the following collision problem from the game of golf. 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:

**Question 1:** Prior to the collision the driver
head was being swung along a circular path because the golfer was
exerting a net torque at the end of the golf club with their hands
to rotate the club. This circular motion implies that there is a
relationship between the linear velocity of the driver head and its
angular velocity. What is the initial angular velocity of the
driver head ω → 1 i in terms of v 1 i, L, and R. Express your
result as a three-component vector.

Answer #1

This problem is very easy once you understand the language of representation of velocity and angular velocity vectors in it.

Also there is a lot of information which is not necessary to solve what is asked in the question still I have diagramatically explained the whole problem before and after the collision to get a picture of what is happening.

The real solution starts from THE THEORY OF CIRCULAR MOTION in the image attached for the detailed solution.

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...

A certain golf club manufacturer advertises that its
new driver (the club you use to hit golf balls off the tee) will
increase the distance that golfers achieve relative to their
current driver. We decide to test this claim by having 15 golfers
hit a drive using the new driver, and then hit one using their
current driver. Here are the data for 15 people, with yardages
using both clubs:
1
2
3
4
5
6
7
8
9
10...

PLEASE DO NOT HANDWRITE
A certain golf club manufacturer advertises that its
new driver (the club you use to hit golf balls off the tee) will
increase the distance that golfers achieve relative to their
current driver. We decide to test this claim by having 15 golfers
hit a drive using the new driver, and then hit one using their
current driver. Here are the data for 15 people, with yardages
using both clubs:
1
2
3
4
5
6...

Step 1: Before the collision, the total momentum is pbefore =
mv0 + 0 where m is the ball’s mass and v0 is the ball’s speed. The
pendulum is not moving so its contribution to the total momentum is
zero. After the collision, the total momentum is pafter = (m + M)
V, where m is the ball’s mass, M is the pendulum mass, and V is the
velocity of the pendulum with the ball stuck inside (see the
picture...

Your task will be to derive the equations describing the
velocity and acceleration in a polar coordinate
system and a rotating polar vector basis for an object in general
2D motion starting from a general
position vector. Then use these expressions to simplify to the case
of non-uniform circular motion, and
finally uniform circular motion.
Here's the time-dependent position vector in a Cartesian coordinate
system with a Cartesian vector
basis: ⃗r(t)=x (t)
̂
i+y(t)
̂
j where x(t) and y(t)...

Consider the bead on a rotating circular hoop system that we saw
in lecture. Recall that R is the radius of the hoop, ω is the
angular velocity of rotation, and m is the mass of the bead that is
constrained to be on the hoop as it rotates about the z-axis. We
found that we could solve the constraints in terms of a single
coordinate θ and that the Cartesian coordinates were given by
x = −R sin(ωt)sinθ, y...

A uniform disk of mass M and radius R is initially rotating
freely about its central axis with an angular speed of ω, and a
piece of clay of mass m is thrown toward the rim of the disk with a
velocity v, tangent to the rim of the disk as shown. The clay
sticks to the rim of the disk, and the disk stops rotating.
33. What is the magnitude of the total angular momentum of the
clay-disk system...

12. Through what angle in degrees does a 31 rpm record turn in
0.27 s
13. Starting from rest, the same torque is applied to a solid
sphere and a hollow sphere. Both spheres have the same size and
mass, and both are rotating about their centers. After some time
has elapsed, which sphere will be rotating faster?
answer choices:
a. hollow sphere
b. They will be rotating equally fast
c. solid sphere
14. In movies, it often happens that...

A playground ride consists of a disk of mass M = 59 kg
and radius R = 1.9 m mounted on a low-friction axle. A
child of mass m = 18 kg runs at speed v = 2.2 m/s
on a line tangential to the disk and jumps onto the outer edge of
the disk.
(b) Relative to the axle, what was the magnitude of the angular
momentum of the child before the collision?
L|C| =
(c) Relative to the...

A solid sphere of uniform density starts from rest and rolls
without slipping a distance of d = 4.4 m down a
θ = 22°incline. The sphere has a
mass M = 4.3 kg and a radius R
= 0.28 m.
1)Of the total kinetic energy of the sphere, what fraction is
translational?
KE
tran/KEtotal =
2)What is the translational kinetic energy of the sphere when it
reaches the bottom of the incline?
KE tran =
3)What is the translational speed...

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