An automobile tire has a radius of 0.330m, and it\'s center moves forward with a

Question

An automobile tire has a radius of 0.330m, and it's center moves forward with a linear speed of v=15.0m/s. (A) determine the angular speed of the wheel. (B) relative to the axle, what is the tangential speed of a point located 0.175m from the axle? An automobile tire has a radius of 0.330m, and it's center moves forward with a linear speed of v=15.0m/s. (A) determine the angular speed of the wheel. (B) relative to the axle, what is the tangential speed of a point located 0.175m from the axle? (A) determine the angular speed of the wheel. (B) relative to the axle, what is the tangential speed of a point located 0.175m from the axle?

Explanation / Answer

Suppose the car travels a distance of 2*pi*r, where r is the radius of the wheel.

(a) in that distance, a point on the edge of the tire will have made one revolution.

The time it takes for the car to travel this distance is
t = d/v = 2*pi*r/v = 2*pi*0.330m/15.0m/s = 0.138 s

The angular velocity of the tire is then

w = 2*pi radians/t = = 2*pi rad/0.138 s = 45.5 rad/sec

(b) at that angular velocity, a point at radius 0.175 m away from the center of the wheel moves tangentially at


v = 0.175 m * 45.5 rad/s = 7.95 m/s

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