Physics: Aparent swings a 18.5 kg child in a circle of radius 1.05m, making 5 revolutions in 13.4s. what centripetal acceleration does the child experience? (unit=m/s^2)

Aparent swings a 18.5 kg child in a circle of radius

GalaxyWolf1895

04.01.2022

$0.146 m/s^{2}$

Explanation:

The centripetal acceleration $a_{c}$ of an object moving in a uniform circular path is given by the following equation:

$a_{c}=\frac{V^{2}}{r}$ (1)

Where:

is the tangential velocity

r=1.05 m is the radius of the circle

On the other hand, the tangential velocity is expressed as:

$V=\omega r$ (2)

Where $\omega$ is the angular velocity, which can be found knowing the child makes 5 revolutions in 13.4s:

$\omega=\frac{5 rev}{13.4 s}=0.37 rev/s$ (3)

Substituting (3) in (2):

V=(0.37 rev/s)(1.05 m) (4)

V=0.39 m/s (5)

Substituting (5) in (1):

$a_{c}=\frac{(0.39 m/s)^{2}}{1.05 m}$ (6)

Finally:

$a_{c}=0.146 m/s^{2}$

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