Chapter 8.2, Problem 7P

To determine

To calculate the speed at which smaller wheel rotates, and speed at which the wheel rotate.

Answer to Problem 7P

The small gear and wheel both rotates at 576 r/min.

Explanation of Solution

Given information:

Diameter of sprocket gear is 8 in.

Diameter of connected gear is 3 in.

Diameter of real wheel 28 in.

Speed of sprocket gear 216 r/min.

Calculation :

Since the product of speed of rotation and circumference of gear is constant, therefore the product of speed of rotation of gear and diameter of gear must be constant.

Assume x be the speed of smaller gear.

From the given condition.

  $\begin{array}{l}216\times 8=k\mathrm{....}\left(i\right)\\ x\times 3=k\mathrm{.....}\left(ii\right)\\ \text{from }\left(i\right)\text{ and }\left(ii\right)\\ 216\times 8=x\times 3\\ x=\frac{216\times 8}{3}\left[\text{divide each side by 3}\right]\\ x=576\end{array}$

Hence, the speed of the smaller gear is 576 r/min.

Since the wheel and gear connected to it rotates about same axis and with same angular speed therefore the wheel also rotates at 576 r/min.