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Sagot :
Answer:
A) Angular velocity = 251.36 rad/s
B) Linear speed = 46.50 m/s
C) Acceleration = 11687.8 m/s^2
Explanations:A) Angular velocity, w = 2400 rpm
Note that:
1 rpm = (2π)/60
Therefore:
2400 rpm = (2π/60) x 2400 rad/s
2400 rpm = 80π rad/s
2400 rpm = 80 x 3.142
2400 rpm = 251.36 rad/s
The angular velocity, w = 251.36 rad/s
B) The relationship between linear speed(v) and angular velocity(w) is:
v = wr
The diameter, d = 0.37m
Radius, r = d/2
r = 0.37/2
r = 0.185m
Substituting r = 0.185m and w = 251.36 rad/s into v = wr:
v = 251.36 x 0.185
v = 46.50 m/s
C) The acceleration a point on the edge of the grinding wheel is the centripetal acceleration, and is given by the formula:
[tex]\begin{gathered} a\text{ = }\frac{v^2}{r} \\ a\text{ = }\frac{46.50^2}{0.185} \\ a\text{ = }\frac{2162.25}{0.185} \\ a\text{ = }11687.8m/s^2 \end{gathered}[/tex]
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