Hello I need help with this question. I know that the formula for angular velocity is w= theta/time. I also know that the answer is 750 rpm. I am just not sure how to get that answer
A truck driver travels at 58 miles per hour. The truck tires have a diameter of 26 inches. What is the angular velocity of the wheels in revolutions per minute (rpm)?
First find the distance covered in one wheel rotation
distance = 2pi(13) = 26pi inches.
truck's speed = 50 miles/hr
= 58(5280)(12)/ 60 inches/min
= 61248 inches/min
Number of rotations per minute = 61248/26pi = 749.84 rotations/min
or your answer of 750 rpm
To find the angular velocity of the truck's wheels in revolutions per minute (rpm), we can use the formula:
w = (v / r) * (60 / (2π))
where:
w is the angular velocity (in rpm),
v is the linear velocity of the truck (in miles per hour),
r is the radius of the wheels (in inches), and
2π is approximately equal to 6.2832.
First, we need to convert the linear velocity from miles per hour to inches per minute since the radius of the wheel is given in inches. To do that, we multiply the linear velocity by a conversion factor, 63,360 inches per mile.
Linear velocity = 58 miles/hour * 63,360 inches/mile / 60 minutes/hour
Next, we find the radius of the wheels by dividing the diameter by 2.
Radius = 26 inches / 2
Now, we can substitute the values into the formula:
w = (58 * 63,360 / 60) / (26 / 2) * (60 / 6.2832)
After simplifying the expression, we get:
w ≈ 750 rpm
Therefore, the angular velocity of the truck's wheels is approximately 750 rpm.