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E=43.66 omega+208.40 h
The total energy,
E, in joules of a metal cylinder with an angular velocity of
omega radians per second and a height of
h meters above the ground is given by the equation. The height and angular velocity are independent. Which of the following expressions is the energy due to the angular velocity?
Choose 1 answer:
(A)
omega
(B) 43.66
(C)
43.66 omega
(D)
43.66 omega+208.40

$E=43.66 \omega+208.40 h$ $\newline$ The total energy, $E$ , in joules of a metal cylinder with an angular velocity of $\omega$ radians per second and a height of $h$ meters above the ground is given by the equation. The height and angular velocity are independent. Which of the following expressions is the energy due to the angular velocity? $\newline$ Choose $1$ answer: $\newline$ (A) $\omega$ $\newline$ (B) $43$ . $66$ $\newline$ (C) $43.66 \omega$ $\newline$ (D) $43.66 \omega+208.40$

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Velocity as a rate of change

Full solution

Q.

E=43.66 \omega+208.40 h

\newline

The total energy,

E

, in joules of a metal cylinder with an angular velocity of

\omega

radians per second and a height of

h

meters above the ground is given by the equation. The height and angular velocity are independent. Which of the following expressions is the energy due to the angular velocity?

\newline

Choose

1

answer:

\newline

(A)

\omega

\newline

(B)

43

.

66

\newline

(C)

43.66 \omega

\newline

(D)

43.66 \omega+208.40

Isolate Omega Term: The equation given is $E = 43.66 \times \omega + 208.40 \times h$ . To find the energy due to the angular velocity, we need to isolate the term that includes $\omega$ , which represents the angular velocity.
Identify Energy Term: Looking at the equation, the term that includes $\omega$ is $43.66 \times \omega$ . This term represents the energy due to the angular velocity because it is the only term that is multiplied by $\omega$ .
Height Independent Term: The term $208.40 \times h$ represents the energy due to the height above the ground and is independent of the angular velocity. Therefore, it is not part of the energy due to the angular velocity.
Correct Energy Expression: The correct expression for the energy due to the angular velocity is $43.66 \times \omega$ . This corresponds to option $(C)$ in the given choices.

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