A hollow spherical shell has mass 8.20 kg and radius 0.215 m . It is initially a

Question

A hollow spherical shell has mass 8.20 kg and radius 0.215 m . It is initially at rest and then rotates about a stationary axis that lies along a diameter with a constant acceleration of 0.890 rad/s2 .

What is the kinetic energy of the shell after it has turned through 6.25 rev ?

session.masteringphysics.com Lafayette Physics 131 - Spring 2016 - Boekelheide and Plenge Signed in as Kurt Bringsjord Help Close Homework #11 Exercise 9.38 Resources «previous 7 of 12 next » Exercise 9.38 Part A A hollow spherical shell has mass 8.20 kg and radius 0.215 m . It is initially at rest and then rotates about a stationary axis that lies alonga diameter with a constant acceleration of 0.890 rad/s2 What is the kinetic energy of the shell after it has turned through 6.25 rev? Express your answer with the appropriate units. LA K 10.7 Submit My Answers Give Up Incorrect; Try Again; 4 attempts remaining Provide Feedback Continue

Explanation / Answer

Given hallow spherical shell of mass m = 8.20 kg, radius r = 0.215 m,
constant angular accleration alphs = 0.890 rad/s2,
initially at rest W1 = 0 rad/s, finally w2 = 6.25 rev=6.25*2pi = 39.27 rad/s

using equations of motion (v2 - u2 = 2as)

   w2^2 = w1^2 +2*alpha*theta
= 0 + 2*0.890*39.27

w^2 = 69.90

w = sqrt(69.90)

w = 8.36 rad/s

now W2 = sqrt(69.90) = 8.36 rad/s
now kinetic energy

   k.e= 1/2 I*w^2; I = 2/3 mR^2 = 2/3 (8.20*0.215^2)
  
   = 1/2 (2/3 (8.20*0.215^2))(69.90)^2 J

   = 617.23 J

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