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san4es73 [151]
2 years ago
12

Consider a solid sphere and a solid disk with the same radius and the same mass. Explain why the solid disk has a greater moment

of inertia than the solid sphere, even though it has the same overall mass and radius.
Physics
1 answer:
Mandarinka [93]2 years ago
8 0

Answer:

Explanation:

In a Solid sphere; the moment of inertia around its geometrical axis can be expressed by using the formula:

\mathtt{I_s = \dfrac{2}{5} M_s R^2_s}

For the solid disk; the moment of inertia around the central axis is:

\mathtt{I_D= \dfrac{1}{2}M_DR_D^2}

Suppose M_D = M_S; then we can say both to be equal to M

As well as R_D = R_S; then that too can be equal to R

Now;

\mathtt{I_s = \dfrac{2}{5} M R^2} --- (1)

\mathtt{I_D= \dfrac{1}{2}MR^2}---(2)

Multiplying equation (1) by 2, followed by dividing it by 2; we have:

\mathtt{I_s= \dfrac{2}{5}MR^2} \times \dfrac{2}{2}

I_s = \dfrac{4}{5} \times \dfrac{1}{2}MR^2 \\ \\ I_s = \dfrac{4}{5}\times I_D \\ \\ I_s > I_D

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disa [49]

Just divide the both, you will get the answer!

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3 0
3 years ago
____ 1. A mineral is inorganic, which means that it contains
Dimas [21]

Answer:

no material that were once part of living things

8 0
3 years ago
A record player turntable initially rotating at 3313 rev/min is braked to a stop at a constant rotational acceleration. The turn
Lelechka [254]

Answer:

a. 16 s b. -1.866 kJ

Explanation:

a. Since the initial rotational speed ω₀= 3313 rev/min = 3313/60 × 2π rad/s = 346.94 rad/s. Its rotational speed becomes ω₁ = 0.75ω₀ in time t = 4 s.

We find it rotational acceleration using α = (ω₁ - ω₀)/t = (0.75ω₀ - ω₀)/t = ω₀(0.75 - 1)/t = -0.25ω₀/t = (-0.25 × 346.94 rad/s)/4 s = -21.68 rad/s².

Since the turntable stops at ω = 0, the time it takes to stop is gotten from

ω = ω₀ + αt and t = (ω - ω₀)/α = (0 - 346.94 rad/s)/-21.68 rad/s² = (-346.94/-21.68) s = 16 s.

So it takes the turntable 16 s to stop.

b. The workdone by the turntable to stop W equals its rotational kinetic energy change.

So, W = 1/2Iω² - 1/2Iω₀² = 1/2 × 0.031 kgm² × 0² - 1/2 × 0.031 kgm² × (346.94 rad/s)² = 0 - 1865.7 J = -1865.7 J = -1.8657 kJ ≅ -1.866 kJ

3 0
3 years ago
1. Calcular la masa de mercurio que pasó de 30 °C hasta 120 °C y absorbió 4400 cal. Calor específico del
timofeeve [1]

Answer:

Masa, m = 0.088 kg

Explanation:

Given the following data;

Temperatura inicial = 30°C

Temperatura final = 120°C

Capacidad calorífica específica = 138J/kg.K

Calor absorbido, Q = 4400 cal.

Para encontrar la masa;

La capacidad calorífica viene dada por la fórmula;

Q = mct

Dónde;

Q representa la capacidad calorífica o la cantidad de calor.

m representa la masa de un objeto.

c representa la capacidad calorífica específica del agua.

dt representa el cambio de temperatura.

dt = T2 - T1

dt = 120 - 30

dt = 90°C to kelvin = 273 + 90 = 363K

Sustituyendo en la fórmula, tenemos;

4400 = m*138*363

4400 = 50094m

m = \frac {4400}{50094}

Masa, m = 0.088 kg

7 0
2 years ago
500 g of water at 90°C is cooled in a freezer. If all the water is converted to ice, what is the amount of heat released when th
KATRIN_1 [288]

Answer:

356 000 J

Explanation:

Total Energy released

= Energy released when water cools to 0 + Energy released when water is converted to ice at 0

= mcT + ml

= (0.5)(4200)(90-0) + (0.5)(334 000)

= 189 000 J + 167 000 J

= <u>3</u><u>5</u><u>6</u><u> </u><u>0</u><u>0</u><u>0</u><u> </u><u>J</u>

4 0
3 years ago
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