Answer:
Explanation:
This problem is based on conservation of angular momentum.
moment of inertia of larger disc I₁ = 1/2 m r² , m is mass and r is radius of disc . I
I₁ = .5 x 20 x 5²
= 250 kgm²
moment of inertia of smaller disc I₂ = 1/2 m r² , m is mass and r is radius of disc . I
I₂ = .5 x 10 x 2.5²
= 31.25 kgm²
3500 rmp = 3500 / 60 rps
n = 58.33 rps
angular velocity of smaller disc ω₂ = 2πn
= 2π x 58.33
= 366.3124 rad /s
applying conservation of angular momentum
I₂ω₂ = ( I₁ +I₂) ω , ω is the common angular velocity
31.25 x 366.3124 = ( 250 +31.25) ω
ω = 40.7 rad / s .
Answer:
M₂ = M then L₂ = L
M₂> M then L₂ = \frac{M}{M_{2}} L
Explanation:
This is a static equilibrium exercise, to solve it we must fix a reference system at the turning point, generally in the center of the rod. By convention counterclockwise turns are considered positive
∑ τ = 0
The mass of the rock is M and placed at a distance, L the mass of the rod M₁, is considered to be placed in its center of mass, which by uniform e is in its geometric center (x = 0) and the triangular mass M₂, with a distance L₂
The triangular shape of the second object determines that its mass can be considered concentrated in its geometric center (median) that tapers with a vertical line if the triangle is equilateral, the most used shape in measurements.
M L + M₁ 0 - m₂ L₂ = 0
M L - m₂ L₂ = 0
L₂ =
L
From this answer we have several possibilities
* if the two masses are equal then L₂ = L
* If the masses are different, with M₂> M then L₂ = \frac{M}{M_{2}} L
The elapsed time when the particle returns to the origin is determined from the ratio of initial velocity and acceleration of the particle.
<h3>Time of motion of the particle</h3>
The time of motion of the particle is calculated by applying Newton's second law of motion.
F = ma
F = m(v)/t
where;
- t is time of motion of the particle
- m is mass of the particle
- v is velocity of the particle
a = v - u/t
v = u + at
when the particle returns to the origin, direction of u, = negative.
final velocity = 0
0 = -u + at
at = u
t = u/a
Learn more about force here: brainly.com/question/12970081
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Producers, consumers, and decomposers help to move matter and energy through ecosystems.
Hope this helps! :)
Answer:
Surely Achilles will catch the Tortoise, in 400 seconds
Explanation:
The problem itself reduces the interval of time many times, almost reaching zero. However, if we assume the interval constant, then it is clear that in two hours Achilles already has surpassed the Tortoise (20 miles while the Tortoise only 3).
To calculate the time, we use kinematic expression for constant speed:

The moment that Achilles catch the tortoise is found by setting the same final position for both (and same time as well, since both start at the same time):
