Question

A particle 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

Answer 1

4.2rad/s

Step-by-step 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

`(Rmu)/(mR^2+0.5MR^2)`

`(0.2*0.1*5)/(0.1*0.2^2+0.5*1*0.2^2)`

ω=4.2rad/s (Approximately)

ω= angular velocity after the collision