A wheel has a radius of 10 inches is rotating with an angular velocity of 2.5 revolutions per second. Find the distance the wheel travels in 15 seconds.
the circumference is 2pi*10 = 62.83cm
So, multiply that by the number of times the wheel turns in 15 seconds.
To find the distance the wheel travels, we need to determine the circumference of the wheel and then multiply it by the number of revolutions.
First, let's calculate the circumference of the wheel using the formula:
C = 2πr
where C is the circumference and r is the radius.
Given that the radius of the wheel is 10 inches, we can substitute this value into the formula:
C = 2π(10)
Now, calculate the circumference:
C = 20π inches
Next, we need to find the distance traveled by the wheel in one revolution, which is the circumference. Since the wheel is rotating with an angular velocity of 2.5 revolutions per second, we can determine the distance traveled per second:
Distance per second = (20π inches) * (2.5 revolutions per second)
Since one revolution corresponds to the circumference (20π inches), we get:
Distance per second = 20π * 2.5 inches
Distance per second = 50π inches
Finally, to find the distance traveled in 15 seconds, multiply the distance per second by the time:
Total distance traveled = Distance per second * Time
Total distance traveled = (50π inches) * (15 seconds)
Total distance traveled = 750π inches
Therefore, the wheel travels approximately 750π inches in 15 seconds.