8. A solid cylinder of mass 20 kg and radius 0.3 m is rotating uniformly at an a

Question

8. A solid cylinder of mass 20 kg and radius 0.3 m is rotating
uniformly at an angular velocity 3.0 rad/s around the fixed axis
through the center O. a) What is the moment of inertia of the
cylinder ? (Given: I = (1/2) M R2 )
b) What is its angular momentum about O ?
c) What is its kinetic energy ?
d) What is the linear speed for a nut on the rim ?
e) How long does it take for the cylinder to make 5 revolutions ?
f) What is the tangential acceleration of the nut ? What is its
centripetal acceleration ?

Explanation / Answer

Moment of inertia of a cylinder is

I = (1/2) MR^2

= (1/2) (20)(0.3)^2

= 0.9 kg m^2

b) angular momentum

   L = I

     = (0.9)(3)

     = 2.7 kg m^2 /s

c) rotation kinetic energy

   K = (1/2) I ^2

   = (1/2)(0.9)(3)^2

     = 4.05J

d) linear speed

    V = R

       = (0.3)(3)

       = 0.9 m/s

e) time taken for 5 rev is

t = 5 ( 2 R ) / V

     = 10 (0.3) / 0.9

     = 10.47s

f ) as the cylinder is moving with constant speed, tangential accleration is zero.

    centripetal acceleration

   a = V^2 / R

     = (0.9)^2 / (0.3)

     = 2.7m/s^2

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