What are the period and (constant) speed of a person on a carousel if the person has an acceleration magnitude of 0.80 m/s2 (direction is toward the center) when she is standing 4.0 m from the axis? (b) what are her acceleration magnitude, and speed if she then moves in to a distance of 2.0 m from the carousel center and the carousel keeps rotating with the same period?

part a)

Centripetal acceleration is given as

Now time period is given as

constant speed is given as

part b)

now when she is at radius r = 2 m

centripetal acceleration is given as

now the linear speed is given as

The value of circular velocity or frequency is .

Explanation:

The charged particle is moving in a circular path.

Let the charge of the particle is . The radius of the circular path is . The velocity of the particle is and it is moving in a magnetic field is .

Now, the magnetic force experienced by the charged particle is,

(assuming the magnetic field is perpendicular to the direction of motion)

Now, the centripetal force experienced by the particle will be,

Velocity of the particle can be written as (in the form of angular velocity) .

Now, equating the magnetic and centripetal force to get the value of circular velocity,

So, the value of circular velocity or frequency is .

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