Question

A shuttle loom is running at 240 picks per minute. The angular velocity of bottom shaft in radian per second is $n\pi$. The value of $n$ is

• A. 4
• B. 5
• C. 6
• D. 8

Hint:

Always remember that one pick corresponds to one full rotation of the bottom shaft in a shuttle loom. Angular velocity is calculated using $\omega = 2\pi N$.

Answer 1

The Correct Option is D

Step 1: Understanding the relationship between picks and shaft rotation.
In a shuttle loom, one pick is inserted for every one complete revolution of the bottom shaft. Therefore, the rotational speed of the bottom shaft is equal to the number of picks per minute.
Step 2: Converting picks per minute to revolutions per second.
Given picks per minute = 240
\[ \text{Revolutions per second} = \frac{240}{60} = 4 \text{ rps} \] Step 3: Converting revolutions per second to angular velocity.
Angular velocity $\omega$ is given by:
\[ \omega = 2\pi \times \text{rps} \] \[ \omega = 2\pi \times 4 = 8\pi \text{ rad/s} \] Step 4: Identifying the value of $n$.
Comparing with $\omega = n\pi$, we get:
\[ n = 8 \] Step 5: Conclusion.
Hence, the value of $n$ is 8.

Answer 2

Instead of jumping straight to the angular velocity formula, we can reason through the timing of the loom cycle directly.

The loom inserts 240 picks every minute, and each pick corresponds to exactly one full revolution of the bottom shaft (since the bottom shaft drives one shedding/picking cycle per revolution). So in one minute (60 seconds), the shaft completes 240 revolutions, meaning the time taken for one revolution is
\[ T = \frac{60 \text{ s}}{240} = 0.25 \text{ s} \]

The angular velocity is related to the period of rotation by
\[ \omega = \frac{2\pi}{T} \]

Substituting the period found above:
\[ \omega = \frac{2\pi}{0.25} = 8\pi \text{ rad/s} \]

Comparing this to the given form \( \omega = n\pi \), we directly read off
\[ n = 8 \]

Therefore, the correct answer is 8.