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(A) For the ingredients to not stick to the wall,the normal force at the top of the drum must be greater than or equal to zero. The limiting condition

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$27.0$

Vedclass · Answer

(A) For the ingredients to not stick to the wall,the normal force at the top of the drum must be greater than or equal to zero. The limiting condition occurs when the normal force is zero,which corresponds to the condition for vertical circular motion where the centripetal force is provided by gravity at the top point.$v = \sqrt{Rg}$Given the radius $R = 1.25\, m$ and $g = 10\, m/s^2$,the angular velocity $\omega$ is:$\omega = \frac{v}{R} = \sqrt{\frac{g}{R}} = \sqrt{\frac{10}{1.25}} = \sqrt{8} = 2.828\, rad/s$.To convert this to revolutions per minute (rpm),we use the relation $\omega (rpm) = \frac{60}{2\pi} 	imes \omega$:$\omega (rpm) = \frac{60}{2 	imes 3.14} 	imes 2.828 \approx 9.55 	imes 2.828 \approx 27.0\, rpm$.Thus,the maximum rotational speed is approximately $27.0\, rpm$.

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