Answer :
Answer:
K = 567.91 J
Explanation:
Given that,
Mass of sphere, m = 18 kg
Radius of a sphere, r = 0.8 m
It makes one complete revolution every 0.4 s.
The speed of center of mass of the sphere is 8 m/s
We need to find the rotational kinetic energy of the sphere. It is given by the formula as follows :
[tex]K=\dfrac{1}{2}I\omega^2[/tex]
I is moment of inertia,
[tex]I=\dfrac{2}{5}mr^2\\\\I=\dfrac{2}{5}\times 18\times (0.8)^2\\\\I=4.608\ kg-m^2[/tex]
[tex]\omega[/tex] is angular speed
[tex]\omega=\dfrac{2\pi }{0.4}\\\\=15.7\ rad/s[/tex]
So,
[tex]K=\dfrac{1}{2}\times 4.608\times (15.7)^2\\\\K=567.91\ J[/tex]
So, the rotational kinetic energy of the sphere is 567.91 J.
The rotational kinetic energy of the sphere is 710.8 J.
Moment of inertia of the sphere
I = ¹/₂mr²
I = 0.5 x 18 x (0.8)²
I = 5.76 kgm²
Angular speed of the sphere
ω = 2πf
ω = 2π x (1/0.4s)
ω = 15.71 rad/s
Rotational kinetic energy
K.E = ¹/₂Iω²
K.E = 0.5 x (5.76) x (15.71)²
K.E = 710.8 J
Thus, the rotational kinetic energy of the sphere is 710.8 J.
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