Question 2 • Common Core Precalculus - MA3112 Quarter 1
Wheel #1 and wheel #2 are spinning at constant rates. A point on the edge of wheel #1 travels with the same linear velocity as a point on the edge of wheel #2.Based on this information, can you conclude that the wheels have the same angular velocity? Explain your answer.
Answer
A
Yes, because angular velocity is directly proportional to linear velocity.
B
Yes, because both of the wheels are spinning at constant rates.
C
No, because determining angular velocity requires knowing the size of each wheel.
D
No, because angular velocity is not related to linear velocity.
Explanation
The relationship between linear speed and angular velocity is v = rω, where r is the wheel’s radius. If the edge points have the same linear velocity, their angular velocities will be the same only if the wheels have the same radius. Since the wheel sizes aren’t given, you can’t determine whether their angular velocities match; choice C is correct.
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