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earnstyle [38]
2 years ago
9

If the resulting trajectory of the charged particle is a circle, what is ω, the angular frequency of the circular motion?

Physics
1 answer:
Komok [63]2 years ago
7 0
For this answer you need to have in mind the following formulas:

Fmag = qvB

Also have in mind that Centripetal acceleration is: ar = v2/R

centripetal force will be :Fc = mv2/R

And velocity is: v = ωR

Remember that the magnetic force is the centripetal force then: 

Fmag = Fc
qvB = mv2/R
qB = mv/R

Next you need to substitute for velocity:

qB = mωR/R
qB = mω

ω = qB/m

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In an engine, a piston oscillates with simple harmonic motion so that its position varies according to the expression x= 5.0 cos
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a)   x = 4.33 m ,   b)  w = 2 rad / s ,  f = 0.318 Hz ,  c) a = - 17.31 cm / s²,  

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Explanation:

In this exercise on simple harmonic motion we are given the expression for motion

          x = 5 cos (2t + π / 6)

they ask us for t = 0

a) the position of the particle

      x = 5 cos (π / 6)

      x = 4.33 m

remember angles are in radians

 

b) The general form of the equation is

          x = A cos (w t + Ф)

when comparing the two equations

         w = 2 rad / s

angular velocity and frequency are related

          w = 2π f

           f = w / 2π

           f = 2 / 2pi

           f = 0.318 Hz

c) the acceleration is defined by

      a == d²x / dt²

      a = - A w² cos (wt + Ф)

for t = 0 ,  we substitute

      a = - 5,0 2² cos (π / 6)

      a = - 17.31 cm / s²

d) El period is

          T = 1/f

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         T =  3.15 s

e) the amplitude

        A = 5.0 cm

3 0
3 years ago
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