How many times does the star spin?

How many times does the star spin?

• A. 2 times
• B. 1 1/2 times
• C. 4 times
• D. 3 times

Answer: (B)

Understanding how rotational motion transfers through a mechanism is the key. When two parts are linked by gears or a belt, the number of spins the driven part makes for each full turn of the driver is set by the gear (or belt) ratio. If the setup gives a 3-to-2 ratio, then for every complete revolution of the driving part, the star rotates 3/2 times, which is 1.5 revolutions. The star has five points, and the silhouette can look the same after rotations of 72 degrees due to its symmetry. But the question is about actual angular displacement, not just when the shape appears identical. So the star ends up spinning one full turn plus another half turn—1 1/2 revolutions—in one full turn of the drive. That’s why the correct answer is 1 1/2.

Understanding how rotational motion transfers through a mechanism is the key. When two parts are linked by gears or a belt, the number of spins the driven part makes for each full turn of the driver is set by the gear (or belt) ratio. If the setup gives a 3-to-2 ratio, then for every complete revolution of the driving part, the star rotates 3/2 times, which is 1.5 revolutions.

The star has five points, and the silhouette can look the same after rotations of 72 degrees due to its symmetry. But the question is about actual angular displacement, not just when the shape appears identical. So the star ends up spinning one full turn plus another half turn—1 1/2 revolutions—in one full turn of the drive. That’s why the correct answer is 1 1/2.