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a wheel is rotating at 3 radians per second, and the wheel has a 71 -inc diameter. To the nearest foot per minute, what is the linear velocity of a point on the rim?

User Mawia HL
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1 Answer

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Final answer:

The linear velocity of a point on the rim of a wheel can be calculated using the formula v = rw. Given the diameter and angular velocity, the radius and rev/min are calculated and substituted into the formula to find the linear velocity. The linear velocity is approximately 532 feet per minute.

Step-by-step explanation:

The linear velocity of a point on the rim of a rotating wheel can be calculated using the formula v = rw, where v is the linear velocity, r is the radius of the wheel, and w is the angular velocity.

Given that the wheel has a diameter of 71 inches, we can calculate the radius by dividing the diameter by 2: r = 71 inches / 2 = 35.5 inches.

Next, we convert the angular velocity of 3 radians per second to rev/min using the conversion factor: w = 3 rad/s * (60 min/1 rev) = 180 rev/min.

Finally, we substitute the values into the formula: v = (35.5 inches) * (180 rev/min) = 6,390 inches/min.

To the nearest foot per minute, the linear velocity of a point on the rim is approximately 532 feet per minute.

User Oskros
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