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harkovskaia [24]
2 years ago
10

A solid disk of mass m1 = 9.3 kg and radius R = 0.22 m is rotating with a constant angular velocity of ω = 31 rad/s. A thin rect

angular rod with mass m2 = 3.9 kg and length L = 2R = 0.44 m begins at rest above the disk and is dropped on the disk where it begins to spin with the disk.
1) What is the initial angular momentum of the rod and disk system?
6.97 kg-m2/s
2) What is the initial rotational energy of the rod and disk system?
108.14 J

3) What is the final angular velocity of the disk?

4) What is the final angular momentum of the rod and disk system?

5) What is the final rotational energy of the rod and disk system?

6) The rod took t = 6.5 s to accelerate to its final angular speed with the disk. What average torque was exerted on the rod by the disk?
Physics
1 answer:
mel-nik [20]2 years ago
5 0
We are given with
<span>m1 = 9.3 kg
R = 0.22 m
ω = 31 rad/s
m2 = 3.9 kg
L = 2R = 0.44 m

The angular momentum is determined using the formula
L  = I w
where I is the moment of inertia

For a solid disk
I = (1/4) MR^2
For a rectangular rod
I = (1/12) ML^2

The rotational energy has the formula
E = (1/2) I w^2

Substitute the given values for getting the answers
</span>
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Answer:

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Explanation:

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4 0
2 years ago
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Tatiana [17]
You can reason it out like this:

-- The car starts from rest, and goes 8 m/s faster every second.

-- After 30 seconds, it's going (30 x 8) = 240 m/s.

-- Its average speed during that 30 sec is  (1/2) (0 + 240) = 120 m/s

-- Distance covered in 30 sec at an average speed of 120 m/s

                                                                           =  3,600 meters .
___________________________________

The formula that has all of this in it is the formula for
distance covered when accelerating from rest:

       Distance = (1/2) · (acceleration) · (time)²

                       = (1/2) ·      (8 m/s²)     · (30 sec)²

                       =      (4 m/s²)          ·      (900 sec²)

                       =            3600 meters.

_________________________________

When you translate these numbers into units for which
we have an intuitive feeling, you find that this problem is
quite bogus, but entertaining nonetheless.

When the light turns green, Andy mashes the pedal to the metal
and covers almost 2.25 miles in 30 seconds.

How does he do that ?

By accelerating at 8 m/s².  That's about 0.82 G  !

He does zero to 60 mph in 3.4 seconds, and at the end
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He doesn't need to worry about getting a speeding ticket.
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3 0
2 years ago
At its lowest setting a centrifuge rotates with an angular speed of ω1 = 250 rad/s. When it is switched to the next higher setti
dalvyx [7]

Answer:

Part(a): The angular acceleration is 5.63~rad~s^{-2}.

Part(b): The angular displacement is 2629~rad.

Explanation:

Part(a):

If \omega_{1},~\omega_{2}~and~\alpha be the initial angular speed, final angular speed and angular acceleration  of the centrifuge respectively, then from rotational kinematic equation, we can write

\alpha = \dfrac{\omega_{2} - \omega_{1}}{t}......................................................(I)

where 't' is the time taken by the centrifuge to increase its angular speed.

Given, \omega_{i} = 250~rad~s^{-1}, \omega_{f} = 750~rad~s^{-1} and t = 9.5~s. From equation (I), the angular acceleration is given by

\alpha = \dfrac{750 - 250}{9.5}~rad~s^{-2} = 5.63~rad~s^{-2}

Part(b):

Also the angular displacement (\Delta \theta) can be written as

&&\Delta \theta = \omega_{1}~t + \dfrac{1}{2}\alpha~t^{2}\\&or,& \Delta \theta = (250 \times 9.5 + \dfrac{1}{2} \times 5.63 \times 9.5^{2})~rad = 2629~rad

8 0
2 years ago
A car is traveling at 20.0 m/s on tires with a diameter of 70.0 cm. The car slows down to a rest after traveling 300.0 m. If the
cupoosta [38]

Answer: deceleration of 1.904\ rad/s^2

Explanation:

Given

Car is traveling at a speed of u=20 m/s

The diameter of the car is d=70 cm

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Using the equation of motion

v^2-u^2=2as\\

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Write acceleration as a=\alpha \cdot r

-\dfrac{2}{3}=\alpha \times 0.35\\\\\alpha =-\dfrac{2}{1.05}\\\\\alpha =-1.904\ rad/s^2

So, the car must be experiencing the deceleration of 1.904\ rad/s^2.

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ser-zykov [4K]
The reaction time of Boris is t(r), so before that, Boris will not have jumped. Thus, H(b)(t) = 0
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2 years ago
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