A line shaft rotating at 200 rpm is connected to a grinding wheel by the pulley assembly shown. If the grinder shaft must turn at 1250 rpm comma what size pulley should be attached to the line​ shaft?

To solve this problem, we can use the concept of **gear ratios** for pulleys. The ratio of the rotational speeds is inversely proportional to the ratio of the pulley diameters.

Let:
- \( N_1 = 200 \, \text{rpm} \) be the rotational speed of the line shaft.
- \( N_2 = 1250 \, \text{rpm} \) be the required rotational speed of the grinding wheel.
- \( D_1 \) be the diameter of the pulley on the line shaft (which we need to find).
- \( D_2 \) be the diameter of the pulley on the grinding wheel.

The relationship between the pulley sizes and rotational speeds is:

\[
\frac{N_1}{N_2} = \frac{D_2}{D_1}
\]

Rearranging to solve for \( D_1 \):

\[
D_1 = D_2 \times \frac{N_2}{N_1}
\]

Now, assuming you know \( D_2 \), the diameter of the pulley on the grinding wheel, you can plug in the values to find \( D_1 \). If not, we need that information to fully calculate \( D_1 \).

Do you know the size of the pulley on the grinding wheel, or would you like me to help with a general ratio?

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Here are 5 related questions:
1. How would the pulley sizes change if the grinding wheel's speed was reduced?
2. Can this principle be used for other mechanical systems, like belts and gears?
3. What happens if the diameter of the line shaft pulley is reduced too much?
4. How do pulley sizes affect torque and power transmission?
5. How would you calculate the belt tension in this pulley system?

**Tip:** The larger the pulley on the line shaft, the slower the connected component will rotate.

A line shaft rotating at 200 rpm is connected to a grinding wheel by the pulley assembly shown. If the grinder shaft must turn at 1250 rpm, what size pulley should be attached to the line shaft?

Learn how to calculate the pulley size needed for a line shaft rotating at 200 RPM to drive a grinding wheel at 1250 RPM. This guide uses the gear ratio formula and covers key mechanical principles suitable for students in Grades 9-12.

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