Answer:
(a) [tex]K_{small}=4839.3J[/tex]
(b) [tex]K_{larger}=17406.4J[/tex]
Explanation:
Given data
The angular velocity of two cylinders ω=257 rad/s
The mass of the two cylinders m=2.88 kg
The radius of small cylinder r₁=0.319 m
The radius of larger cylinder r₂=0.605 m
For Part (a)
The rotational kinetic energy of the cylinder is given by:
[tex]K=\frac{1}{2}Iw^2[/tex]
Where I is rotational of inertia of solid cylinder about its central axis.
So
[tex]K=\frac{1}{2}Iw^2\\ K=\frac{1}{2}(1/2mr^2)w^2[/tex]
Substitute the given values
So
[tex]K_{small}=\frac{1}{4}(2.88kg)(0.319)^2(257rad/s)^2 \\K_{small}=4839.3J[/tex]
For Part (b)
[tex]K=\frac{1}{2}Iw^2\\ K=\frac{1}{2}(1/2mr_{2}^2)w^2[/tex]
Substitute the given values
[tex]K_{larger}=\frac{1}{4}mr_{2}^2w^2\\ K_{larger}=\frac{1}{4}(2.88kg)(0.605m)^2(257rad/s)^2\\ K_{larger}=17406.4J[/tex]
