The new oscillation frequency of the pendulum clock is 1.14 rad/s.
The given parameters;
- <em>Mass of the pendulum, = M </em>
- <em>Length of the pendulum, = L</em>
- <em>Initial angular speed, </em>
<em> = 1 rad/s</em>
The moment of inertia of the rod about the end is given as;
![I_i = \frac{1}{3} ML^2](https://tex.z-dn.net/?f=I_i%20%3D%20%5Cfrac%7B1%7D%7B3%7D%20ML%5E2)
The moment of inertia of the rod between the middle and the end is calculated as;
![I_f = \int\limits^L_{L/2} {r^2\frac{M}{L} } \, dr = \frac{M}{3L} [r^3]^L_{L/2} = \frac{M}{3L} [L^3 - \frac{L^3}{8} ] = \frac{M}{3L} [\frac{7L^3}{8} ]= \frac{7ML^2}{24}](https://tex.z-dn.net/?f=I_f%20%3D%20%5Cint%5Climits%5EL_%7BL%2F2%7D%20%7Br%5E2%5Cfrac%7BM%7D%7BL%7D%20%7D%20%5C%2C%20dr%20%3D%20%5Cfrac%7BM%7D%7B3L%7D%20%5Br%5E3%5D%5EL_%7BL%2F2%7D%20%3D%20%20%5Cfrac%7BM%7D%7B3L%7D%20%5BL%5E3%20-%20%5Cfrac%7BL%5E3%7D%7B8%7D%20%5D%20%3D%20%5Cfrac%7BM%7D%7B3L%7D%20%5B%5Cfrac%7B7L%5E3%7D%7B8%7D%20%5D%3D%20%5Cfrac%7B7ML%5E2%7D%7B24%7D)
Apply the principle of conservation of angular momentum as shown below;
![I _i \omega _i = I _f \omega _f\\\\\frac{ML^2}{3} (1 \ rad/s)= \frac{7ML^2}{24} \times \omega _f\\\\\frac{24 \times ML^2}{3 \times 7 ML^2} (1 \ rad/s)= \omega _f\\\\1.14 \ rad/s = \omega _f](https://tex.z-dn.net/?f=I%20_i%20%5Comega%20_i%20%3D%20I%20_f%20%5Comega%20_f%5C%5C%5C%5C%5Cfrac%7BML%5E2%7D%7B3%7D%20%281%20%5C%20rad%2Fs%29%3D%20%5Cfrac%7B7ML%5E2%7D%7B24%7D%20%5Ctimes%20%5Comega%20_f%5C%5C%5C%5C%5Cfrac%7B24%20%5Ctimes%20ML%5E2%7D%7B3%20%5Ctimes%207%20ML%5E2%7D%20%281%20%5C%20rad%2Fs%29%3D%20%5Comega%20_f%5C%5C%5C%5C1.14%20%5C%20rad%2Fs%20%3D%20%5Comega%20_f)
Thus, the new oscillation frequency of the pendulum clock is 1.14 rad/s.
Learn more about moment of inertia of uniform rod here: brainly.com/question/15648129
Answer:
<em>The electric field can either oscillates in the z-direction, or the y-direction, but must oscillate in a direction perpendicular to the direction of propagation, and the direction of oscillation of the magnetic field.</em>
Explanation:
Electromagnetic waves are waves that have an oscillating magnetic and electric field, that oscillates perpendicularly to one another. Electromagnetic waves are propagated in a direction perpendicular to both the electric and the magnetic field. If the wave is propagated in the x-direction, then the electric field can either oscillate in the y-direction, or the z-direction but must oscillate perpendicularly to both the the direction of oscillation of the magnetic field, and the direction of propagation of the wave.
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Answer:
v = 384km/min
Explanation:
In order to calculate the speed of the Hubble space telescope, you first calculate the distance that Hubble travels for one orbit.
You know that 37000 times the orbit of Hubble are 1,280,000,000 km. Then, for one orbit you have:
![d=\frac{1,280,000,000km}{37,000}=34,594.59km](https://tex.z-dn.net/?f=d%3D%5Cfrac%7B1%2C280%2C000%2C000km%7D%7B37%2C000%7D%3D34%2C594.59km)
You know that one orbit is completed by Hubble on 90 min. You use the following formula to calculate the speed:
![v=\frac{d}{t}=\frac{34,594.59km}{90min}=384.38\frac{km}{min}\approx384\frac{km}{min}](https://tex.z-dn.net/?f=v%3D%5Cfrac%7Bd%7D%7Bt%7D%3D%5Cfrac%7B34%2C594.59km%7D%7B90min%7D%3D384.38%5Cfrac%7Bkm%7D%7Bmin%7D%5Capprox384%5Cfrac%7Bkm%7D%7Bmin%7D)
hence, the speed of the Hubble is approximately 384km/min
Answer:Reflection
Explanation:
The throwing back of a sound wave without absorbing it is called reflection
In acoustic reflection of sound is termed as echo i.e. sound arrived at the listener after a particular delay depending upon the position of barrier to the observer.
The reflection of sound is used in many devices like megaphone, trumpets, etc. It is also used in auditorium such that the ceiling of the auditorium is curved for multiple reflections of sound so that sound can be reached at every corner of the auditorium.