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Elza [17]
3 years ago
8

A uniform circular disk of moment of inertia 8.0 kg m2 is rotating at 4.0 rad/s. A small lump of mass 1.0 kg is dropped on the d

isk and sticks to it at a distance of 1.0 m from the axis of rotation. What is the new rotational speed of the combined system?
Physics
1 answer:
Butoxors [25]3 years ago
7 0

The new rotational speed of the combined system is 32 rad/s

<u>Explanation:</u>

Given-

Moment of Inertia, I = 8 kg m²

speed of rotation, ω = 4 rad/s

Mass of the lump = 1 kg

distance = 1 m

New rotational speed = ?

We know,

When the lump is dropped on the rotating disc then the angular momentum remains conserved.

Angular Momentum of the disc, Lₐ = Iω

Angular momentum of the lump, L ₓ = mvR

Since the angular momentum remains conserved,

Lₐ = Lₓ

8 X 4 = 1 X v X 1

New rotational speed, v = 32 rad/s

Therefore, the new rotational speed of the combined system is 32 rad/s.

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Explanation:

Given,

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\begin{gathered}\large{\boxed{\sf{P \: = \: \dfrac{1}{f}}}} \\ \\ \rightarrow {\sf{P \: = \: \dfrac{1}{-25}}}\end{gathered}

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\begin{gathered}\rightarrow {\sf{P \: = \: \dfrac{1}{\dfrac{-25}{100}}}} \\ \\ \rightarrow {\sf{P \: = \: \dfrac{-100}{25}}} \\ \\ \rightarrow {\sf{P \: = \:- 4}} \\ \\ \underline{\sf{\therefore \: Power \: of \: Concave \: lens \: is \: - \: 4D}}\end{gathered}

8 0
1 year ago
Convert the volume 8.06 in.3 to m3, recalling that1in. =2.54cmand100cm=1m. Answer in units of m3.
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Answer: 8.06 in³=1.321 x 10⁻⁴ m³
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