Question

A gear system is made of a larger gear that has a radius of 30 centimeters is turning a smaller gear that has a diameter of 10 centimeters. If 400 Nm of torque is exerted on the large gear, how much torque is applied to the smaller gear?​

Answer 1

The torque applied to the smaller gear is 1200 Nm.

Step-by-step explanation:

To find the torque applied to the smaller gear, we need to consider the relationship between torque and gear ratios.

The gear ratio between two gears is defined as the ratio of the number of teeth on the larger gear to the number of teeth on the smaller gear. In this case, we are given the radii of the larger and smaller gears.

The gear ratio (GR) can be calculated using the formula:

GR = Radius of Larger Gear / Radius of Smaller Gear

Let's calculate the gear ratio:

Radius of Larger Gear = 30 cm

Radius of Smaller Gear = 10 cm

GR = 30 cm / 10 cm = 3

The gear ratio is 3, which means that for every one revolution of the larger gear, the smaller gear will rotate three times.

Now, the torque is inversely proportional to the gear ratio. In other words, the torque applied to the smaller gear will be three times the torque applied to the larger gear.

Given that the torque applied to the larger gear is 400 Nm, the torque applied to the smaller gear can be calculated as:

Torque of Smaller Gear = Gear Ratio * Torque of Larger Gear

Torque of Smaller Gear = 3 * 400 Nm = 1200 Nm

Therefore, the torque applied to the smaller gear is 1200 Nm.