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Westkost [7]
3 years ago
9

Which of the following is NOT true? a. The higher the moment of inertia, the greater the resistance to changes in angular veloci

ty. b. The higher the moment of inertia, the slower something will roll down an incline. c. The lower the moment of inertia, the easier it is to change the angular velocity. d. The lower the moment of inertia, the slower something will roll down an incline.
Physics
1 answer:
kaheart [24]3 years ago
4 0

Answer:

Explanation:

The moment of inertia is the integral of the product of the squared distance by the mass differential. Is the mass equivalent in the rotational motion

a) True. When the moment of inertia is increased, more force is needed to reach acceleration, so it is more difficult to change the angular velocity that depends proportionally on the acceleration

b) True. The moment of inertia is part of the kinetic energy, which is composed of a linear and an angular part. Therefore, when applying the energy conservation theorem, the potential energy is transformed into kinetic energy, the rotational part increases with the moment of inertia, so there is less energy left for the linear part and consequently it falls slower

c) True. The moment of inertial proportional to the angular acceleration, when the acceleration decreases as well. Therefore, a smaller force can achieve the value of acceleration and the change in angular velocity. Consequently, less force is needed is easier

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2,666.67cm^3

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series RC circuit is built with a 15 kΩ resistor and a parallel-plate capacitor with 18-cm-diameter electrodes. A 18 V, 36 kHz s
andre [41]

Answer:

d=1.84\ mm

Explanation:

<u>Capacitance</u>

A two parallel-plate capacitor has a capacitance of

\displaystyle C=\frac{\epsilon_o A}{d}

where

\epsilon_o=8.85\cdot 10^{-12}\ F/m

A = area of the plates = \pi r^2

d = separation of the plates

\displaystyle d=\frac{\epsilon_o A}{C}=\frac{\epsilon_o \pi r^2}{C}

We need to compute C. We'll use the circuit parameters for that. The reactance of a capacitor is given by

\displaystyle X_c=\frac{1}{wC}

where w is the angular frequency

w=2\pi f=2\pi \cdot 36000=226194.67\ rad/s

Solving for C

\displaystyle C=\frac{1}{wX_c}

The reactance can be found knowing the total impedance of the circuit:

Z^2=R^2+X_c^2

Where R is the resistance, R=15 K\Omega=15000\Omega. Solving for Xc

X_c^2=Z^2-R^2

The magnitude of the impedance is computed as the ratio of the rms voltage and rms current

\displaystyle Z=\frac{V}{I}

The rms current is the peak current Ip divided by \sqrt{2}, thus

\displaystyle Z=\frac{\sqrt{2}V}{I_p}

I_p=0.65\ mA/1000=0.00065\ A

Now collect formulas

\displaystyle X_c^2=Z^2-R^2=\left(\frac{\sqrt{2}V}{I_p}\right)^2-R^2

Or, equivalently

\displaystyle X_c=\sqrt{\frac{2V^2}{I_p^2}-R^2}

\displaystyle X_c=\sqrt{\frac{2\cdot 18^2}{0.00065^2}-15000^2}

X_c=36176.34\ \Omega

The capacitance is now

\displaystyle C=\frac{1}{226194.67\cdot 36176.34}=1.22\cdot 10^{-10}\ F

The radius of the plates is

r=18\ cm/2=9 \ cm = 0.09 \ m

The separation between the plates is

\displaystyle d=\frac{8.85\cdot 10^{-12} \cdot \pi\cdot 0.09^2}{1.22\cdot 10^{-10}}

d=0.00184\ m

\boxed{d=1.84\ mm}

8 0
2 years ago
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