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NikAS [45]
2 years ago
7

A solid, uniform disk of mass M and radius a may be rotated about an axis parallel to the disk axis, at variable distances from

the center of the disk.
What is Tmin, the minimum period of the pendulum?
Physics
1 answer:
cricket20 [7]2 years ago
6 0

Answer:

the function varies linearly with the radius of the disk, so the smallest period is zero for a radius of zero centimeters

Explanation:

This system performs a simple harmonic movement where the angular velocity is given by

         w = √ k / I

Where k is the constant recovered from the axis of rotation and I is the moment of inertia of the disk

The expression for the moment of inertia is

           I = 1/2 m r²

Angular velocity, frequency and period are related

         w = 2π f = 2π / T

Substituting

             2π / T = √ k / I

             T = 2π √ I / k

             T = 2π √ (½ m r² / k)

             T = (2π √m / 2k)   r

 

We can see that the function varies linearly with the radius of the disk, so the smallest period is zero for a radius of zero centimeters

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scZoUnD [109]
Momentum is conserved.

p = m₁v₁ + m₂v₂ = constant

Momentum before the collision(kick):

p = 80 * 0 + 4 * 0 = 0

Momentum after the collision:
p = 80 * v₁ + 4 * 15 = 0

Solve for v₁.

3 0
2 years ago
A 4.0-m-diameter playground merry-go-round, with a moment of inertia of 350 kg⋅m2 is freely rotating with an angular velocity of
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Answer:

v = 4.375\,\frac{m}{s}

Explanation:

The situation of the system Ryan - merry-go-round is modelled after the Principle of the Angular Momentum Conservation:

(350\,kg\cdot m^{2})\cdot (1.5\,\frac{rad}{s} ) - (2\,m)\cdot (60\,kg)\cdot v = 0\,kg\cdot \frac{m^{2}}{s}

The initial speed of Ryan is:

v = 4.375\,\frac{m}{s}

5 0
2 years ago
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An elevator has a weight of 14,700 N and has an acceleration of –0.30 m/s2. The free-body diagram shows the forces acting on the
qwelly [4]

14250. I just took it

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2 years ago
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A 6.70 −μC particle moves through a region of space where an electric field of magnitude 1500 N/C points in the positive x direc
Alborosie

The given question is incomplete. The complete question is as follows.

A 6.70 −μC particle moves through a region of space where an electric field of magnitude 1500 N/C points in the positive x direction, and a magnetic field of magnitude 1.25 T points in the positive z direction.

A) If the net force acting on the particle is 6.21 \times 10^{-3} N in the positive x direction, find the components of the particle's velocity. Assume the particle's velocity is in the x-y plane.

Enter your answers numerically separated by commas.

Explanation:

The given data is as follows.

           Q = 6.50 \times 10^{-6} C

           E = 1300 N/C in the +x direction

           B = 1.02 T in the +z direction

and,    F_{net} = 6.25 \times 10^{-3} N in the +x direction

Also,       F_{net} = F_{E} - F_{b}

                         = qE - qvB

Now, we will calculate the value of v as follows.

             v = (\frac{1}{B}) \times (E - \frac{F_{net}}{q})

                 = (\frac{1}{1.02 T}) \times (1300 - \frac{6.25 \times 10^{-3}}{6.50 \times 10^{-6}})

                v = 458.507 m/s

Using the value for velocity, we need to know which direction it's going.

You know +x direction for E, +z direction for B and +x for F_{net}.

Using the right hand rule where:

your right thumb goes toward the F_{net}, then your index finger points to B (z direction) Then curl your middle, ring, and pink 90 angle. This shows where v is going which is -y direction.

Thus, we can conclude that v_{x}, v_{y}, v_{z} = 0, -(458.507), 0.

8 0
2 years ago
A solenoid of length 18 cm consists of closely spaced coils of wire wrapped tightly around a wooden core. The magnetic field str
Kisachek [45]

Answer:

B_2 = 1.71 mT

Explanation:

As we know that the magnetic field near the center of solenoid is given as

B = \frac{\mu_0 N i}{L}

now we know that initially the length of the solenoid is L = 18 cm and N number of turns are wounded on it

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now we pulled the coils apart and the length of solenoid is increased as L = 21 cm

so we have

\frac{B_1}{B_2} = \frac{L_2}{L_1}

now plug in all values in it

\frac{2.0 mT}{B_2} = \frac{21}{18}

B_2 = 1.71 mT

3 0
2 years ago
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