ASVAB (Armed Services Vocational Aptitude Battery)Mechanical Comprehension (MC)Medium
A mechanic is using a gear system to reduce the speed of a motor while increasing its torque. The driving gear has 40 teeth and rotates at 120 RPM. If the driven gear needs to rotate at 30 RPM, how many teeth must the driven gear have?
- A160 teeth
- B10 teeth
- C40 teeth
- D80 teeth
Show answer & explanationAnswer & explanation
Correct answer: A. 160 teeth
The relationship between the number of teeth and rotational speed in a gear system is inverse. (Teeth_driver / Teeth_driven) = (RPM_driven / RPM_driver). So, (40 / X) = (30 / 120). Solving for X gives X = (40 * 120) / 30 = 160 teeth.
Why the other options are wrong
- B. This would result in a much higher driven gear speed, not a reduction.
- C. This would mean no change in speed, which contradicts the goal of reducing speed.
- D. This would result in a driven gear speed of 60 RPM, not the desired 30 RPM.
Gear Ratio (Speed/Teeth)
The ratio of the number of teeth on two meshing gears, which determines the change in speed and torque between them. An inverse relationship exists between teeth count and rotational speed.
- More teeth on the driven gear reduce speed and increase torque.
- Fewer teeth on the driven gear increase speed and reduce torque.
- Formula: N_driver / N_driven = RPM_driven / RPM_driver.
Memory trick: Teeth and Turns: More teeth, less turn speed (but more twisting power).