Question

In the gear train shown, gear 3 is carried on arm 5, Gear 3 mashes with gear 2 and gear 4. The number of teeth on gear 2, 3 and 4 are 60, 20, and 100, respectively. If gear 2 is fixed and gear 4 rotates with an angular velocity of 100 rpm in the counterclockwise direction, the angular speed of arm 5 (in rpm) is

• A. 166.7 counterclockwise
• B. 166.7 clockwise
• C. 62.5 counterclockwise
• D. 62.5 clockwise

Answer 1

The correct option is C 62.5 counterclockwise

Gear	2	3	4
Number of teeth	60	20	100
Speed in rpm	+N (clockwise)	$\frac{-N\times 60}{20}$ anticlockwise	$\frac{-N\times 60\times 20}{20\times 100}$ (anticlockwise)
Let speed of arm by y rpm (y+ clockwise)	N+y	$\frac{-N\times 60}{20}+y$	$\frac{-N\times 60}{100}+y$

Given:

Gear 2 is fixed:

$\therefore N+y=0$ [$\therefore N=-y$]

Gear 4 rotates 100 rpm counter clockwise.

$-\frac{N\times 60}{100}+y=-100$

$+y\times 0.6+y=-100$

$y=\frac{-100}{1.6}=-62.5\text{rpm}$

Hence, the angular speed of the arm is 62.5 rpm (counterclockwise).