What is the angular velocity of the front wheels in rpm?

[tiger21]

1. 1. The rear wheels of a tractor are 4 ft in diameter and turn at 20 rpm.

a. How fast is the tractor going (ft. per sec.)?
b. The front wheels have a diameter of only 1.8 ft. What is the linear velocity of a point on their tire treads?
c. What is the angular velocity of the front wheels in rpm?

 

[HallsofIvy]

You aren't going to even try? What is the circumference of the wheels? If they turn at 20 rpm per minute, what distance do the wheels move (at every revolution, of course, they move a distance equal to the circumference) in one minute? How far do they move in one second?
b) and c) are much the same. As the tractor moves forward, the front wheels will have to move the same distance as the rear wheels. Since the circumference of the front wheels is smaller, the front wheels will have to turn faster to cover the same distance.

 

[Architeuthis Dux]

a. To determine the speed of the tractor in feet per second, we can use the formula: speed = distance / time. Since the wheels are turning at 20 rpm, we can convert this to revolutions per second by dividing by 60 (since there are 60 seconds in a minute). This gives us 20/60 = 0.33 revolutions per second. Now, we can determine the distance that the tractor travels in one revolution by multiplying the circumference of the wheel (π*diameter) by the number of revolutions. This gives us (3.14*4) * 0.33 = 4.13 feet per second. Therefore, the tractor is traveling at a speed of 4.13 feet per second.

b. To determine the linear velocity of a point on the front wheel's tire treads, we can use the same formula: speed = distance / time. In this case, the distance is the circumference of the front wheel (π*1.8) and the time is still 0.33 seconds (since the front wheels are also turning at 20 rpm). This gives us (3.14*1.8) * 0.33 = 1.88 feet per second. Therefore, the linear velocity of a point on the front wheel's tire treads is 1.88 feet per second.

c. The angular velocity of the front wheels can be determined by dividing the linear velocity (1.88 feet per second) by the radius of the front wheel (0.9 feet). This gives us 1.88/0.9 = 2.09 radians per second. To convert this to rpm, we can multiply by 60 (since there are 2π radians in one revolution). This gives us 2.09 * 60 = 125.4 rpm. Therefore, the angular velocity of the front wheels is 125.4 rpm.