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Calculate the angular velocity of a 0.300 m radius car tire when the car travels at 15.0 m/s.
A12.5 rad/s
B45.0 rad/s
C50.0 rad/s
D5.00 rad/s
Answer & Solution
Correct answer: C. 50.0 rad/s
1. Because the tire rolls without slipping, the tire rim's linear speed equals the car's speed, so v = 15.0 m/s.
2. Angular velocity is omega = v / r.
3. Substituting the known values, omega = 15.0 m/s / 0.300 m.
4. That division gives omega = 50.0 rad/s.
5. 12.5 rad/s is the value for a much larger 1.20 m tire at the same speed, and 45.0 rad/s and 5.00 rad/s come from arithmetic slips in the division.
_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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