An automobile tire has a radius of 0.335 m, and its center moves forward with a linear speed of v = 24.1 m/s. (a) Determine the angular speed of the wheel. (b) Relative to the axle, what is the tangential speed of a point located 0.243 m from the axle?
Circumference=pi*2r=3.14*0.67=2.1=2.1 m.
Va = 24.1m/s * 6.28rad/2.1m=72.1 rad/s.
b. V = (0.243/0.335) * 28m/s = 20.3 m/s.
To determine the angular speed of the wheel, we can use the formula:
angular speed (ω) = linear speed (v) / radius (r)
(a) Given that the radius of the tire is 0.335 m and the linear speed is 24.1 m/s, we can substitute these values into the formula:
ω = 24.1 m/s / 0.335 m
ω ≈ 71.94 radians/s
Therefore, the angular speed of the wheel is approximately 71.94 radians/s.
Now, to determine the tangential speed of a point located 0.243 m from the axle relative to the axle, we can use the formula:
tangential speed = angular speed (ω) * radius (r)
(b) Given that the radius of the tire is 0.243 m and the angular speed is 71.94 radians/s, we can substitute these values:
tangential speed = 71.94 radians/s * 0.243 m
tangential speed ≈ 17.47 m/s
Therefore, the tangential speed of a point located 0.243 m from the axle, relative to the axle, is approximately 17.47 m/s.