Question

Calculate the moment of inertia of the angle section about the X-axis. (See Lesson 7)​

Answer 1

Answer:

Read this excerpt from The Great Fire.

While this was happening near the fire, more errors were taking place a mile and a half away. Chicago had recently renovated its fire alarm system, making it one of the best in the nation. Each firehouse had a watchman who scanned the immediate neighborhood for flames or smoke during the night. Overlooking the entire city was a watchman in the cupola of the Courthouse, one hundred feet above the ground. If a fire was spotted, an alarm was telegraphed (either from the firehouse or from one of the many alarm boxes situated around town) to the Courthouse; the Courthouse watchman then relayed the location of the blaze to the firehouses nearest to it. For added security, the giant Courthouse bell was also rung. Because of the drought, special Insurance Patrols had been organized and Benjamin Bullwinkle was appointed to head them. These patrols roamed the streets at night, ready to put out small fires with chemical extinguishers and turn in alarms for bigger blazes. While this system sounds very cumbersome to us, back in 1871 it was considered quite speedy and efficient.

Which quotation best reflects the main idea of this paragraph?

“While this was happening near the fire, more errors were taking place a mile and a half away.”

“Chicago had recently renovated its fire alarm system, making it one of the best in the nation.”

“Because of the drought, special Insurance Patrols had been organized and Benjamin Bullwinkle was appointed to head them.”

“These patrols roamed the streets at night, ready to put out small fires with chemical extinguishers and turn in alarms for bigger blazes.”

Answer 2

Answer :

The moment of inertia along the x axis  = 4.2209 x 10⁶ mm.

Explanation:

Moment of Inertia :

Moment of inertia is defined as the resisting angular acceleration of the body or, which means that the sum of the product of the mass of that body with the squared of the distance of the axis of rotation.

• Moment of inertia is basically chosen along a particular axis.

• It depends on the mass distributed around that axis of rotation.

Considering, the vertical rectangle which has a height of 100mm and the breadth is of 12.5mm

then, h₁ = 100mm

and b₁ = 12.5mm

and considering the horizontal cut off portion if the rectangle to the ground :

the height will be 12.5mm and breadth will be 100 - 12.5 mm = 87.5mm

So, h₂ = 12.5mm

and b₂ = 87.5mm

Now, we know that the moment of inertia along the x-axis =

Iₓ = $\frac{b1(h1)^3}{3}$ + $\frac{b2(h2)^3}{3}$

or, Iₓ = (12.5 x (100)³)/3 + (87.5 x (12.5)³)/3

or, Iₓ  = 4.2209 x 10⁶ mm.

Therefore, the moment of inertia along the x axis  = 4.2209 x 10⁶ mm.

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