What is the speed of a spur gear with 42 teeth driven by a pinion gear with 14 teeth turning at 420 RPM?

To find the speed of the spur gear, you can use the relationship between the number of teeth on the gears and their rotational speeds. This relationship is given by the equation:

[ \text{Speed of Pinion} \times \text{Teeth of Pinion} = \text{Speed of Spur Gear} \times \text{Teeth of Spur Gear} ]

In this scenario, the pinion gear has 14 teeth and is turning at 420 RPM. The spur gear has 42 teeth. Plugging these values into the equation allows you to rearrange it to solve for the speed of the spur gear:

[ 420 , \text{RPM} \times 14 = \text{Speed of Spur Gear} \times 42 ]

Calculating the left side:

[ 420 \times 14 = 5880 ]

Now, you can set up the equation:

[ 5880 = \text{Speed of Spur Gear} \times 42 ]

To find the speed of the spur gear, divide both sides by 42:

[ \text{Speed of Spur Gear} = \frac{5880}{42} ]

Doing the division gives:

[ \text{Speed