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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?

Respuesta :

part a)

Centripetal acceleration is given as

[tex]a_c = \omega^2 R[/tex]

[tex]0.80 = \omega^2 * 4[/tex]

[tex]\omega = 0.45 rad/s[/tex]

Now time period is given as

[tex]T = \frac{2\pi}{\omega}[/tex]

[tex]T = \frac{2\pi}{0.45}[/tex]

[tex]T = 14.04 s[/tex]

constant speed is given as

[tex]v = R \omega[/tex]

[tex]v = 4* 0.45 = 1.8 m/s[/tex]

part b)

now when she is at radius r = 2 m

centripetal acceleration is given as

[tex]a_c = \omega^2 R[/tex]

[tex]a_c = 0.45^2 * 2 = 0.405 m/s^2[/tex]

now the linear speed is given as

[tex]v = r\omega[/tex]

[tex]v = 2 * 0.45 = 0.9 m/s[/tex]

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