In Fig. 10-54, wheel \( A \) of radius \( r_{A}=10 \mathrm{~cm} \) is coupled by belt \( B \) to...

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In Fig. 10-54, wheel \( A \) of radius \( r_{A}=10 \mathrm{~cm} \) is coupled by belt \( B \) to wheel \( C \) of radius \( r_{C}=25 \mathrm{~cm} \). The angular speed of wheel \( A \) is increased from rest at a
\( B \)
constant rate of \( 2.0 \mathrm{rad} / \mathrm{s}^{2} \).
Figure 10-54
Find the time needed for
wheel \( C \) to reach an angular speed of \( 100 \mathrm{rev} / \mathrm{min} \), assuming the belt does not slip. (Hint: If the belt does not slip, the linear speeds at the two rims must be equal.)
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