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An earth mover has tires of radius 1.20 m, four times the radius of a 0.300 m car tire. If both vehicles travel at the same 15.0 m/s, how does the earth mover tire's angular velocity compare with the car tire's 50.0 rad/s?
AIt is 12.5 rad/s, one fourth as large
BIt is 200 rad/s, four times as large
CIt is 50.0 rad/s, exactly the same
DIt is 62.5 rad/s, larger by 12.5 rad/s
Answer & Solution
Correct answer: A. It is 12.5 rad/s, one fourth as large
1. Angular velocity is omega = v / r, so at fixed speed v it is inversely proportional to the radius r.
2. Substituting the earth mover's values, omega = 15.0 m/s / 1.20 m.
3. That division gives omega = 12.5 rad/s.
4. Since 1.20 m is four times 0.300 m, the angular velocity is one fourth of the car tire's 50.0 rad/s, confirming the larger tire spins more slowly at the same road speed.
5. 200 rad/s would result from multiplying rather than dividing by the radius ratio, and 62.5 rad/s comes from adding rather than scaling the two angular velocities.
_Source: OpenStax College Physics (CC BY 4.0), Ch 6 "Uniform Circular Motion and Gravitation", section 6.1 Rotation Angle and Angular Velocity_
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