A cylinder has inner and outer radii of #12 cm# and #18 cm#, respectively, and a mass of #6 kg#. If the cylinder's frequency of rotation about its center changes from #7 Hz# to #6 Hz#, by how much does its angular momentum change?

1 Answer
Apr 17, 2016

Answer:

#Delta P=-28,8pi#

Explanation:

#"1-calculate the changing of the angular velocity"#
#"2-calculate the moment of inertia for cylinder"#
#"3-calculate changing of the angular momentum"#

#"1)....................................................................."#
#f_i=7Hz" initial frequency"#
#f_l=6Hz" last frequency"#
#Delta omega=omega_l-omega_i" changing of the angular velocity"#

#omega_l=2*pi*f_l" "omega_l=2*pi*6" "omega_l=12pi " "(rad)/s#

#omega_i=2*pi*f_i" "omega_i=2*pi*7" "omega_i=14pi" "(rad)/s#

#Delta omega=12pi-14pi#

#Delta omega=-2pi" "(rad)/s#
#2)........................................................................#
#I=1/2*m(r_1^2+r_2^2)#
#"moment of inertia for cylinder which has inner and outer radius"#

m=6kg

#r_1=12 cm=0,12 m#
#r_1^2=1,44#

#r_2=18cm=0,18m#
#r_2^2=3,24#
#I=1/2*6(1,44+3,24)#

#I=3*4,68#

I=14,04

#3)............................................................................#
#Delta P=I*Delta omega" angular momentum change"#
#Delta P=-14,4*2pi#

#Delta P=-28,8pi#