Question

given that the average rotational speed of a rotating object is approximately 1.21 rad/s, and the radius of the object is 20.1 m, find the translational speed of the object in miles per minute. notes: 1 mile = 1609.3 m; 1 minute = 60 s. multiple choice 652 miles per minute 471 miles per minute 0.619 miles per minute 0.907 miles per minute

Explanation:

Step1: Recall the formula for translational speed (linear speed) from rotational speed. The formula is \( v = \omega r \), where \( \omega \) is the angular (rotational) speed and \( r \) is the radius.

\( v = 1.21 \, \text{rad/s} \times 20.1 \, \text{m} \)

Step2: Calculate the linear speed in meters per second.

\( v = 1.21 \times 20.1 = 24.321 \, \text{m/s} \)

Step3: Convert meters per second to meters per minute. Since there are 60 seconds in a minute, multiply by 60.

\( v = 24.321 \, \text{m/s} \times 60 \, \text{s/min} = 1459.26 \, \text{m/min} \)

Step4: Convert meters per minute to miles per minute. Use the conversion factor \( 1 \, \text{mile} = 1609.3 \, \text{m} \), so divide by 1609.3.

\( v = \frac{1459.26}{1609.3} \approx 0.907 \, \text{miles per minute} \)

Answer:

0.907 miles per minute (the option: 0.907 miles per minute)