Aparticle of mass m = 0.10 kg and speed v0 = 5.0 m/s collides and sticks to the end of a uniform solid cylinder of mass m = 1.0 kg and radius r = 20 cm. if the cylinder is initially at rest and is pivoted about a frictionless axle through its center, what is the final angular velocity (in rad/s) of the system after the collision?

a. 8.1
b. 2.0
c. 6.1
d. 4.2
e. 10

4.2rad/s

Explanation:

momentum is the product of the mass of a body and its velocity

conservation of angular momentum

total momentum before collision =total momentum after collision

L1=L2

initial momentum

L1=r*p=Rmu

final angular momentum

L1=I*ω=

(mR^2+0.5mR^2)ω

Angular momentum equals

Rmu=(mR^2+0.5MR^2)ω

to  solve for ω

ω=4.2rad/s  (Approximately)

ω= angular velocity after the collision

option number c is the right answer.