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Nadya [2.5K]
3 years ago
11

A majorette in the Rose Bowl Parade tosses a baton into the air with an initial angular velocity of 2.5 rev/s. If the baton unde

rgoes a constant acceleration while airborne of 0.2 rev/s2 and its angular velocity is 0.8 rev/s when the majorette catches it, how many revolutions does it make in the air?
Physics
1 answer:
oksian1 [2.3K]3 years ago
4 0

Answer:

14 rev

Explanation:

w_{o} = initial angular velocity = 2.5 revs⁻¹

w = final angular velocity = 0.8 revs⁻¹

\alpha = Angular acceleration = - 0.2 revs⁻²

\theta = Angular displacement

Using the equation

w^{2} = w_{o}^{2} + 2 \alpha \theta\\0.8^{2} = 2.5^{2} + 2 (- 0.2) \theta\\ \theta = 14 rev

So the number of revolutions are 14

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There's a nasty wrinkle here that's kind of sneaky, and makes the work harder than it should be.

Look at the first question.  There's a number there that's dropped in so quietly that you're almost sure to miss it, but it changes the whole landscape of both of these problems.   That's where it says

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When the question talks about hanging a weight, it tells the <em>centimeter mark on the stick</em> where the weight is tied.  To solve the problem, we have to first figure out <em>how far that is from the pivot</em>, then calculate how far from the pivot to put the weight on the other side, and finally <u><em>what centimeter mark that is</em></u> on the stick.      

How to solve the problems:

-- The "moment" of a weight is (the weight) x (its distance from the pivot) .

-- To balance the stick, (the sum of the moments on one side) = (the sum of the moments on the other side).

= = = = = = = = = =  

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(500 gm) x (distance from pivot) = 4,800 gm-cm

Distance from pivot = (4,800 gm-cm) / (500 gm)  =  9.6 cm

The 500 gm has to hang 9.6 cm to the right of the pivot.  But that's not the answer to the problem.  They want to know what mark on the stick to hang it from.  The pivot is at the 50cm mark.  The 500gm has to hang 9.6 cm to the right of the pivot.  That's the <em>59.6 cm</em> mark on the stick.

= = = = =

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one weight:  120gm, hanging from the 25cm mark.

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