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An iron disc spins about its axis at a constant angular velocity omega. As it is slowly heated from 20 deg C to 50 deg C with omega held fixed, what is the percentage change in the linear speed of a particle on the rim? (linear expansion coefficient of iron = 1.2 x 10⁻⁵ per deg C.)

1. 0.036% increase
2. 0.036% decrease
3. 0.36% increase
4. 0.36% decrease

Correct answer: 0.036% increase

Solution

Heating expands the radius by Delta r/r = alpha*Delta T = 1.2e-5 * 30 = 3.6e-4 = 0.036%, and since v = omega r with omega constant, v increases by 0.036%.

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