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Accelerate a rotating wheel

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Again, very vague... But the number should kind of represent the "work" required.

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Why we use chess pieces? Well... we like chess, we like playing around with \(\LaTeX\)-fonts, we wanted symbols that need less space than six stars in a table-column... But in your layouts, you are of course free to indicate the difficulty of the exercise the way you want.

That being said... How "difficult" is an exercise? It depends on many factors, like what was being taught etc.
In physics exercises, we try to follow this pattern:

Level 1 - One formula (one you would find in a reference book) is enough to solve the exercise. Example exercise

Level 2 - Two formulas are needed, it's possible to compute an "in-between" solution, i.e. no algebraic equation needed. Example exercise

Level 3 - "Chain-computations" like on level 2, but 3+ calculations. Still, no equations, i.e. you are not forced to solve it in an algebraic manner. Example exercise

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Level 5 -
Level 6 -

Exercise

https://texercises.com/exercise/accelerate-a-rotating-wheel/

Question

Solution

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Need help? Yes, please!

The following quantities appear in the problem: Winkelgeschwindigkeit / Kreisfrequenz \(\omega\) / Winkelbeschleunigung \(\alpha\) / Winkel \(\theta\) /

The following formulas must be used to solve the exercise: \(\omega^2 = \omega_0^2 + 2\alpha(\gamma-\gamma_0) \quad \)

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Exercise:
abcliste abc A wheel initially rotates at awzO. The wheel is now accelerated uniformly at aaO so that its orbital period is then waO. By what angle does it rotate? abc Another wheel completes initially a rotation every bwzO. This time the wheel is accelerated uniformly at abO -- until it has rotated gbO. At what angular velocity does it then rotate? abc Yet another wheel initially rotates at cwzO. The wheel should now be accelerated uniformly to wcO orbital period -- so that it rotates exactly gcO during the acceleration. How strong must this angular acceleration be? abcliste

Solution:
abcliste abc gamma fracomega^-omega_^alpha fracqtywa^-qtyawz^ aa gam approx gamS abc omega sqrtalphagamma + omega_^ sqrt ab gb + qtybwz^ wb approx wbS abc alpha fracomega^-omega_^gamma fracqtywc^-qtycwz^ gc ac approx acS abcliste

Meta Information

\(\LaTeX\)-Code

Contained in these collections:

Kinematik Kreis 3. Formel by TeXercises

6 | 6
Kinematik der Kreisbewegung 1 by uz

6 | 6

Attributes & Decorations

Branches	Circular Motion, Kinematics
Tags	beschleunigung, drehung, kinematik, kreis, kreisbewegung, rad, winkelbeschleunigung, winkelgeschwindigkeit
Content image
Difficulty	(1, default)
Points	3 (default)
Language	(English)
Type	Calculative / Quantity
Creator	uz
Decoration
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Link