Answer: [tex]0.0833 m/s^{2}[/tex]
Explanation:
The centripetal acceleration [tex]a_{c}[/tex] of an object moving in a uniform circular motion is given by the following equation:
[tex]a_{c}=\omega^{2} r[/tex]
Where:
[tex]\omega=42 \frac{rev}{min} \frac{1 min}{60 s}=0.7 \frac{rev}{s}[/tex] is the angular velocity of the speck of clay
[tex]r=\frac{d}{2}[/tex] is the radius of the potter's wheel, being [tex]d=34 cm \frac{1}m{100 cm}=0.34 m[/tex] its diameter (hence [tex]r=\frac{0.34 m}{2}=0.17 m[/tex] )
[tex]a_{c}=(0.7 \frac{rev}{s})^{2} 0.17 m[/tex]
[tex]a_{c}=0.0833 m/s^{2}[/tex]
The (centripetal) acceleration of the speck of clay is [tex]3.29 m/s^2[/tex]
Explanation:
The centripetal acceleration of an object in uniform circular motion is given by
[tex]a=\omega^2 r[/tex]
where
[tex]\omega[/tex] is the angular speed of the object
r is the distance of the object from the centre of rotation
In this problem, we have:
[tex]\omega=42 rpm[/tex] is the angular speed
Converting into radians/second,
[tex]\omega=42 rpm \cdot \frac{2\pi rad/rev}{60 s/min}=4.40 rad/s[/tex]
The diameter of the wheel is
d = 34 cm = 0.34 m
So the distance of the speck of clay from the axis of rotation is equal to the radius:
[tex]r=\frac{d}{2}=0.17 m[/tex]
Therefore, the centripetal acceleration is
[tex]a=(4.40)^2(0.17)=3.29 m/s^2[/tex]
Learn more about centripetal acceleration:
brainly.com/question/2562955
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