Question

A sphere of uniform density with mass 26 kg and radius 0.5 m is spinning, making one complete revolution every 0.4 s. the center of mass of the sphere has a speed of 5 m/s. (a) what is the rotational kinetic energy of the sphere? 801.09 incorrect: your answer is incorrect. j (b) what is the total kinetic energy of the sphere?

Answer 1

(a) Rotational kinetic energy = 1/2Iω^2

Where, I = cmr^2 = 2/5*26*0.5^2 = 2.6 kg/m^2; ω=1 rev/0.4 sec = 2.5 rev/sec = 2.5*2π rad/s = 15.71 rad/s

Therefore, Rotational KE = 1/2*2.6*15.71^2 = 320.76 J

(b) Total kinetic energy = Linear KE+ Rotational KE
Linear KE = 1/2mv^2 = 0.5*26*5^2 = 325 J
Then,
Total KE of sphere = 320.76+325 = 645.76 J