E1. Work-Energy Theorem: differential form - Revision history

Bros at 08:01, 21 May 2025

2025-05-21T08:01:43Z

2025-05-20T12:19:09Z

✏️ EXAMPLE E1-1.2: pendulum

2025-05-20T12:18:31Z

✏️ EXAMPLE E1-1.2: pendulum

← Older revision		Revision as of 12:18, 20 May 2025
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	\|A particle '''P''' of mass m hangs from an inextensible thread of length L attached to the ceiling. The assembly oscillates in a vertical plane fixed to the ground. <u>We want to calculate the power of all the forces acting on the particle in two different reference frames: the ground and a platform rotating relative to the ground with a constant angular velocity <math>\Omega_0</math>. </u>		\|A particle '''P''' of mass m hangs from an inextensible thread of length L attached to the ceiling. The assembly oscillates in a vertical plane fixed to the ground. <u>We want to calculate the power of all the forces acting on the particle in two different reference frames: the ground and a platform rotating relative to the ground with a constant angular velocity <math>\Omega_0</math>. </u>
	\|}		\|}
			<br>

			<br>

	<u>Ground reference frame:</u> Since it is a Galilean reference frame, '''P''' is only subjected to interaction forces.		<u>Ground reference frame:</u> Since it is a Galilean reference frame, '''P''' is only subjected to interaction forces.

2025-05-20T12:17:45Z

✏️ EXAMPLE E1-1.2: pendulum

← Older revision		Revision as of 12:17, 20 May 2025
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	\|}		\|}

	~~<math>\vspace{8cm}</math>~~

	<u>Platform reference frame: </u> It is a non Galilean reference frame, and the transportation force on '''P''' has to be taken into account.		<u>Platform reference frame: </u> It is a non Galilean reference frame, and the transportation force on '''P''' has to be taken into account.

2025-05-20T12:17:33Z

✏️ EXAMPLE E1-1.2: pendulum

← Older revision		Revision as of 12:17, 20 May 2025
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	:[[File:ExE1-2-1-eng.png\|thumb\|left\|180px\|link=]]		:[[File:ExE1-2-1-eng.png\|thumb\|left\|180px\|link=]]
	\|A particle '''P''' of mass m hangs from an inextensible thread of length L attached to the ceiling. The assembly oscillates in a vertical plane fixed to the ground. <u>We want to calculate the power of all the forces acting on the particle in two different reference frames: the ground and a platform rotating relative to the ground with a constant angular velocity <math>\Omega_0</math>. </u>		\|A particle '''P''' of mass m hangs from an inextensible thread of length L attached to the ceiling. The assembly oscillates in a vertical plane fixed to the ground. <u>We want to calculate the power of all the forces acting on the particle in two different reference frames: the ground and a platform rotating relative to the ground with a constant angular velocity <math>\Omega_0</math>. </u>
			\|}

	<u>Ground reference frame:</u> Since it is a Galilean reference frame, '''P''' is only subjected to interaction forces.		<u>Ground reference frame:</u> Since it is a Galilean reference frame, '''P''' is only subjected to interaction forces.

2025-05-20T12:17:07Z

✏️ EXAMPLE E1-1.2: pendulum

← Older revision		Revision as of 12:17, 20 May 2025
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	\|}		\|}

	<math>\~~hspace~~{8cm}</math>		<math>\vspace{8cm}</math>

	<u>Platform reference frame: </u> It is a non Galilean reference frame, and the transportation force on '''P''' has to be taken into account.		<u>Platform reference frame: </u> It is a non Galilean reference frame, and the transportation force on '''P''' has to be taken into account.

2025-05-20T12:16:55Z

✏️ EXAMPLE E1-1.2: pendulum

← Older revision		Revision as of 12:16, 20 May 2025
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	\|}		\|}

	<math>\hspace{~~2cm~~}</math>		<math>\hspace{8cm}</math>

	<u>Platform reference frame: </u> It is a non Galilean reference frame, and the transportation force on '''P''' has to be taken into account.		<u>Platform reference frame: </u> It is a non Galilean reference frame, and the transportation force on '''P''' has to be taken into account.

2025-05-20T12:16:29Z

✏️ EXAMPLE E1-1.2: pendulum

← Older revision		Revision as of 12:16, 20 May 2025
Line 215:		Line 215:
	\|}		\|}

			<math>\hspace{2cm}</math>

	<u>Platform reference frame: </u> It is a non Galilean reference frame, and the transportation force on '''P''' has to be taken into account.		<u>Platform reference frame: </u> It is a non Galilean reference frame, and the transportation force on '''P''' has to be taken into account.

2025-05-20T12:15:55Z

✏️ EXAMPLE E1-1.2: pendulum

← Older revision		Revision as of 12:15, 20 May 2025
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	<math>\dot{\Ws}_\Es^\text{weight}=(\nearrow\Ls\dot{\theta}\cdot(\downarrow \ms\gs)=-\ms\gs\Ls\dot{\theta}\sin\theta</math>		<math>\dot{\Ws}_\Es^\text{weight}=(\nearrow\Ls\dot{\theta}\cdot(\downarrow \ms\gs)=-\ms\gs\Ls\dot{\theta}\sin\theta</math>
			\|}

	\|}

	<u>Platform reference frame: </u> It is a non Galilean reference frame, and the transportation force on '''P''' has to be taken into account.		<u>Platform reference frame: </u> It is a non Galilean reference frame, and the transportation force on '''P''' has to be taken into account.

2025-05-20T12:15:26Z

✏️ EXAMPLE E1-1.2: pendulum