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3 years ago

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A wheel at rest gains an angular momentum of 10.7kgm²/s in 8s. if the moment if inertia of the wheel is 2.2kgm², how many revolu

tions will be made before the wheel attains an angular velocity of 30rad/s

1 answer:

EleoNora [17]3 years ago

3 0

Answer:

Revolutions made before attaining angular velocity of 30 rad/s:

θ = 3.92 revolutions

Explanation:

Given that:

L(final) = 10.7 kgm²/s

L(initial) = 0

time = 8s

<h3>Find Torque:</h3>

Torque is the rate of change of angular momentum:

$T = \frac{L(final)-L(initial)}{t}\\T = \frac{10.7-0}{8}\\T=1.34 Nm$

<h3>Find Angular Acceleration:</h3>

We know that

T = Iα

α = T/I

where I = moment of inertia = 2.2kgm²

α = 1.34/2.2

α = 0.61 rad/s²

<h3>Find Time 't'</h3>

We know that angular equation of motion is:

ω²(final) = ω²(initial) +2αθ

(30 rad/s)² = 0 + 2(0.61 rad/s²)θ

θ = (30 rad/s)²/ 2(0.61 rad/s²)

θ = 24.6 radians

Convert it into revolutions:

θ = 24.6/ 2π

θ = 3.92 revolutions

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In a thin film experiment, a wedge of air is used between two glass plates. If the wavelength of the incident light in air is 48

cluponka [151]

Answer:

The thickness is $\Delta y = 2.4 *10^{-6} \ m$

Explanation:

From the question we are told that

The wavelength is $\lambda = 480 \ nm = 480*10^{-9} \ m$

The first order of the dark fringe is $m_1 = 16$

The second order of dark fringe considered is $m_2 = 6$

Generally the condition for destructive interference is mathematically represented as

$y = \frac{m \lambda}{2}$

Here y is the path difference between the central maxima(i.e the origin) and any dark fringe

So the path difference between the 16th dark fringe and the 6th dark fringe is mathematically represented as

$y_1 - y_2 = \Delta y = \frac{m_1 \lambda}{2} - \frac{m_2 \lambda}{2}$

=> $y_1 - y_2 = \Delta y = \frac{16 *480*10^{-9}}{2} - \frac{6 *480*10^{-9}}{2}$

=> $y_1 - y_2 = \Delta y = 5 (480*10^{-9})$

=> $\Delta y = 2.4 *10^{-6} \ m$

8 0

3 years ago

Points A (-5,6), B (2,-2), and C (-6,-3) are placed in three different quadrants of a Cartesian coordinate system. Convert each

AURORKA [14]

Answer: A ( $\sqrt{61}$ ,309.8°)

B (2 $\sqrt{2}$ , 315°)

C ( $3\sqrt{5}$ , 26.56°)

Explanation: To transform rectangular coordinates into polar coordinates use:

$r=\sqrt{x^{2}+y^{2}}$ and $\theta=tan^{-1}(\frac{y}{x})$

For point A:

$r=\sqrt{(-5)^{2}+6^{2}}$

$r=\sqrt{61}$

$\theta=tan^{-1}(\frac{6}{-5})$

$\theta=tan^{-1}(-1.2)$

$\theta=-50.2$ °

Point A is in the II quadrant, so we substract the angle for 360° since it is in degrees:

$\theta=360-50.2$

$\theta=$ 309.8°

Polar coordinates for point A is ( $\sqrt{61}$ , 309.8°)

For point B:

$r=\sqrt{2^{2}+(-2)^{2}}$

$r=\sqrt{8}$

$r=2\sqrt{2}$

$\theta=tan^{-1}(\frac{-2}{2} )$

$\theta=tan^{-1}(1)$

$\theta=-45$ °

Point B is in IV quadrant, so:

$\theta=360-45$

$\theta=$ 315°

Polar coordinates for point B is ( $2\sqrt{2}$ , 315°)

For point C:

$r=\sqrt{(-6)^{2}+(-3)^{2}}$

$r=\sqrt{45}$

$r=3\sqrt{5}$

$\theta=tan^{-1}(\frac{-3}{-6} )$

$\theta=tan^{-1}(0.5)$

$\theta=$ 26.56°

Polar coordinates for point C is ( $3\sqrt{5}$ , 26.56°)

3 0

3 years ago

The net electric charge of an amber rod which has been rubbed with fur is called negative Group of answer choices because amber

bonufazy [111]

Answer:

The right option is option E. None of the answer choices given are totally correct.

Explanation:

All insulators normally have an equal amount of positive and negative charges distributed on their surface.

The amber rod (an insulator) is called negative because after the coming together with fur (another insulator), the amber rod rubs off electrons from the fur onto itself and has an overall more negatively charged particles than positively charged particles on its surface.

The fur in turn becomes positive because it has more positive charges than negative on its surface.

So, the convention allows the now rubbed off amber rod to be called negative.

So, it is evident that none of the answer choices are totally correct, the right answer is more of a mix of some of the answer choices and more!

Hope this helps!!

3 0

3 years ago

An Atwood's machine consists of two different masses, both hanging vertically and connected by an ideal string which passes over

Tasya [4]

Answer:

V₁ = √ (gy / 3)

Explanation:

For this exercise we will use the concepts of mechanical energy, for which we define energy n the initial point and the point of average height and / 2

Starting point

Em₀ = U₁ + U₂

Em₀ = m₁ g y₁ + m₂ g y₂

Let's place the reference system at the point where the mass m1 is

y₁ = 0

y₂ = y

Em₀ = m₂ g y = 2 m₁ g y

End point, at height yf = y / 2

$E_{mf}$ = K₁ + U₁ + K₂ + U₂

$E_{mf}$ = ½ m₁ v₁² + ½ m₂ v₂² + m₁ g $y_{f}$ + m₂ g $y_{f}$

Since the masses are joined by a rope, they must have the same speed

$E_{mf}$ = ½ (m₁ + m₂) v₁² + (m₁ + m₂) g $y_{f}$

$E_{mf}$ = ½ (m₁ + 2m₁) v₁² + (m₁ + 2m₁) g $y_{f}$

How energy is conserved

Em₀ = $E_{mf}$

2 m₁ g y = ½ (m₁ + 2m₁) v₁² + (m₁ + 2m₁) g $y_{f}$

2 m₁ g y = ½ (3m₁) v₁² + (3m₁) g y / 2

3/2 v₁² = 2 g y -3/2 g y

3/2 v₁² = ½ g y

V₁ = √ (gy / 3)

5 0

3 years ago

Wooden handles on knives do not require maintenance.<br> TRUE<br> FALSE

Olenka [21]

Answer: false

Explanation:

You have to make sure it doesn’t stay wet

5 0

3 years ago