Solve the problem.
-A wheel is rotating 720 times per minute. Through how many degrees does a point on the edge of the wheel move in $\frac { 1 } { 4 }$ seconds?
A) $810 ^ { \circ }$
B) $72 ^ { \circ }$
C) $1080 ^ { \circ }$
D) $270 ^ { \circ }$

Question

Quizplus · Accepted Answer

A wheel rotating 720 times per minute means it completes 720 revolutions each minute. To find how many degrees it rotates in $\frac{1}{4}$ seconds, first convert the rotation rate to seconds: $720 \text{ revolutions per minute} = 720 \times 60 = 43200 \text{ degrees per second}$ (since each revolution is $360^\circ$). Then, for $\frac{1}{4}$ second, the rotation is $43200 \times \frac{1}{4} = 10800 \text{ degrees}$. However, there was a mistake in my calculation: it should be $720 \text{ revolutions per minute} = 12 \text{ revolutions per second}$ (since $720 \div 60 = 12$), and each revolution is $360^\circ$, so in $\frac{1}{4}$ second, it rotates $12 \times 360 \times \frac{1}{4} = 1080^\circ$.

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