A lawn tractor tire turns at 65rpm and has a radius of 13cm. What is the linear speed of the tractor in m/s?
angular velocity = omega = 65 revs/min * 2 pi radians/rev * 1 min/60 s = 6.81 radians/second
R = 13 cm * 1 m/100 cm = 0.13 m
omega R = 6.81*.13 = .885 m/s
Thank you
To find the linear speed of the tractor in m/s, we can use the formula:
Linear speed = angular speed × radius
First, let's convert the radius from centimeters to meters. Since there are 100 centimeters in one meter, the radius in meters would be 13 cm ÷ 100 = 0.13 m.
Next, we need to convert the angular speed from revolutions per minute (rpm) to radians per second (rad/s). Since there are 2π radians in one revolution and 60 seconds in one minute, the angular speed in rad/s would be:
65 rpm × (2π rad/1 rev) × (1 min/60 s) ≈ 6.80 rad/s
Now, we can calculate the linear speed using the formula:
Linear speed = 6.80 rad/s × 0.13 m ≈ 0.884 m/s
Therefore, the linear speed of the lawn tractor is approximately 0.884 m/s.