A wheel with a 15-inch diameter is turning at the rate of 60 revolutions per minute. To the nearest inch per minute, what is the linear speed of a point on the rim?
speed=distance/time=PI*diameter/(1/60 min)
= PI * diameter*60 inches/minute
To find the linear speed of a point on the rim of the wheel, we need to calculate the circumference of the wheel and then multiply it by the number of revolutions per minute.
The circumference of a circle can be calculated using the formula C = πd, where C is the circumference and d is the diameter. In this case, the diameter is 15 inches, so the circumference is:
C = π(15 inches) = 15π inches
Next, we need to find the linear speed by multiplying the circumference by the number of revolutions per minute. In this case, the wheel is rotating at 60 revolutions per minute, so the linear speed is:
Linear Speed = (15π inches) * (60 revolutions/minute)
To find the answer to the question, we can use the approximate value of π as 3.14. Plugging in the values:
Linear Speed ≈ (15 * 3.14 inches) * (60 revolutions/minute)
Simplifying further, we have:
Linear Speed ≈ 471 inches/minute
Therefore, to the nearest inch per minute, the linear speed of a point on the rim of the wheel is 471 inches/minute.