Solve the problem.
-A wheel is rotating at 8 radians per sec, and the wheel has a 51 -inch diameter. To the nearest foot per minute, what is the speed of a point on the rim?
A) $1010 \mathrm { ft }$ per min
B) $1020 \mathrm { ft }$ per min
C) $1025 \mathrm { ft }$ per min
D) $1015 \mathrm { ft }$ per min

Question

Quizplus · Accepted Answer

To find the speed of a point on the rim, we use the formula $v = r\omega$, where $v$ is the linear speed, $r$ is the radius of the wheel, and $\omega$ is the angular speed. Given the diameter is 51 inches, the radius $r = \frac{51}{2} = 25.5$ inches. Converting inches to feet, $r = \frac{25.5}{12}$ feet. Given $\omega = 8$ radians per second, we find $v = \frac{25.5}{12} \times 8$. To convert to feet per minute, multiply by 60: $v = \frac{25.5}{12} \times 8 \times 60$. Calculating this gives $v \approx 1020$ feet per minute.

Solve the Problem 1010ft1010 \mathrm { ft }1010ft Per Min B) 1020ft1020 \mathrm { ft }1020ft

Solve the Problem $1010 \mathrm { ft }$ Per Min
B) $1020 \mathrm { ft }$