A solid cylinder has a mass of 8 pounds and a radius of 2 feet.calculate the radius gyration of the cylinder?

The radius of gyration (k) of a solid cylinder is given by the formula:

k = √(I / m)

where I is the moment of inertia of the cylinder and m is the mass of the cylinder.

The moment of inertia of a solid cylinder about its central axis is given by the formula:

I = (1/2) * m * r^2

Substitute the given values into the formula:

I = (1/2) * 8 * 2^2
I = (1/2) * 8 * 4
I = 16

Now, substitute the values of I and m into the formula for the radius of gyration:

k = √(16 / 8)
k = √2
k ≈ 1.41 feet

Therefore, the radius of gyration of the cylinder is approximately 1.41 feet.

The radius of gyration (k) of a solid cylinder can be calculated using the formula:

k = √(I/M)

where:

- I is the moment of inertia
- M is the mass

Determine the Moment of Inertia (I)

For a solid cylinder, the moment of inertia about its central axis is given by:

I = (1/2) - M - r^2

where:

- M is the mass (8 pounds)
- r is the radius (2 feet)

Substitute the values:

I = (1/2) - 8 lb - (2 ft)^2 = 16 lb-ft^2

Calculate the Radius of Gyration (k)

Now, substitute the moment of inertia and mass into the formula:

k = √(16 lb-ft^2 / 8 lb) = √2 ft

Therefore, the radius of gyration of the solid cylinder is √2 feet.