Ask question

Ask question

All categories

3 years ago

7

A rotator has a weight of 100lb with a centroidal radius of gyration of 9 in. Determine the moment of inertia about the center o

f gravity for the rotator.

1 answer:

Ronch [10]3 years ago

8 0

Answer:

8100 lbin²

Explanation:

Moment or inertia is expressed using the formula

I = mr²

M is the mass of the body

r is the radius of gyration

Given

W = 100lb

r = 9in

Required

Moment of inertia

I = Wr²

I = 100(9)²

I = 100×81

I = 8100lbin²

Hence the moment of inertia about the center of gravity for the rotator is

8100 lbin²

You might be interested in

Calculate the viscosity(dynamic) and kinematic viscosity of airwhen

nikitadnepr [17]

Answer:

(a) dynamic viscosity = $1.812\times 10^{-5}Pa-sec$

(b) kinematic viscosity = $1.4732\times 10^{-5}m^2/sec$

Explanation:

We have given temperature T = 288.15 K

Density $d=1.23kg/m^3$

According to Sutherland's Formula dynamic viscosity is given by

${\mu} = {\mu}_0 \frac {T_0+C} {T + C} \left (\frac {T} {T_0} \right )^{3/2}$ , here

μ = dynamic viscosity in (Pa·s) at input temperature T,

$\mu _0$ = reference viscosity in(Pa·s) at reference temperature T0,

T = input temperature in kelvin,

$T_0$ = reference temperature in kelvin,

C = Sutherland's constant for the gaseous material in question here C =120

$\mu _0=4\pi \times 10^{-7}$

$T_0$ = 291.15

$\mu =4\pi \times 10^{-7}\times \frac{291.15+120}{285.15+120}\times \left ( \frac{288.15}{291.15} \right )^{\frac{3}{2}}=1.812\times 10^{-5}Pa-s$ when T = 288.15 K

For kinematic viscosity :

$\nu = \frac {\mu} {\rho}$

$kinemic\ viscosity=\frac{1.812\times 10^{-5}}{1.23}=1.4732\times 10^{-5}m^2/sec$

3 0

3 years ago

An engineer designs a new bus that can drive 30 miles per gallon of fuel. Which of the following was likely one of the client’s

Marat540 [252]

What are the options?

7 0

3 years ago

Read 2 more answers

Consider CO at 500 K and 1000 kPa at an initial state that expands to a final pressure of 200 kPa in an isentropic manner. Repor

REY [17]

Answer:

$T_2=315.69k$

Explanation:

Initial Temperature $T_1=500K$

Initial Pressure $P_1=1000kPa$

Final Pressure $P_2=200kPa$

Generally the gas equation is mathematically given by

$\frac{T_2}{T_1}=\frac{P_2}{P_1}^{\frac{n-1}{n}}$

Where

n for $CO=1.4$

Therefore

$\frac{T_2}{500}=\frac{200}{1000}^{\frac{1.4-1}{1.4}}$

$T_2=315.69k$

7 0

3 years ago

A circular column is fixed at the base and not supported at the top. If the column needs to be 15ft and hold 10kips, what is the

muminat

Answer:

The required size of column is length = 15 ft and diameter = 4.04 inches

Explanation:

Given;

Length of the column, L = 15 ft

Applied load, P = 10 kips = 10 × 10³ Psi

End condition as fixed at the base and free at the top

thus,

Effective length of the column, $\L_e$ = 2L = 30 ft = 360 inches

now, for aluminium

Elastic modulus, E = 1.0 × 10⁷ Psi

Now, from the Euler's critical load, we have

$P =\frac{\pi^2EI}{L_e^2}$

where, I is the moment of inertia

on substituting the respective values, we get

$10\times10^3 =\frac{\pi^2\times1.0\times10^7\times I}{360^2}$

or

I = 13.13 in⁴

also for circular cross-section

I = $\frac{\pi}{64}\times d^4$

thus,

13.13 = $\frac{\pi}{64}\times d^4$

or

d = 4.04 inches

The required size of column is length = 15 ft and diameter = 4.04 inches

3 0

3 years ago

Consider insulation on a circular pipe For the same thickness and type of insulation, the thermal resistance of the insulation i

leonid [27]

Answer:

b). The same for all pipes independent of the diameter

Explanation:

We know,

$R_{conduction}=\frac{ln(\frac{r_{2}}{r_{1}})}{2\pi LK}$

$R_{convection}=\frac{1}{h(2\pi r_{2}L)}$

From the above formulas we can conclude that the thermal resistance of a substance mainly depends upon heat transfer coefficient,whereas radius has negligible effects on heat transfer coefficient.

We also know,

Factors on which thermal resistance of insulation depends are :

1. Thickness of the insulation

2. Thermal conductivity of the insulating material.

Therefore from above observation we can conclude that the thermal resistance of the insulation is same for all pipes independent of diameter.

5 0

3 years ago