PhysicsChapter 1: Physical Quantities and Measurement
1.7.3 Screw Gauge
A screw gauge
Explanation level
Some measurements in physics require even greater precision than a vernier caliper can provide. For example, measuring the diameter of a thin wire or the thickness of a metal sheet requires an instrument that can measure to a fraction of a millimetre. The screw gauge is designed for this purpose, using the principle of a screw to achieve very fine measurements.
Definition
A screw gauge is a length measuring device used for measurements even smaller than those possible with a vernier caliper. It measures a fraction of the smallest division on a scale by rotating a circular scale over a linear (main) scale.
Main Idea
The main idea is precision through rotation. A screw gauge uses a screw mechanism to convert a small rotation of a circular scale into a very small linear movement along a main scale. This allows it to measure extremely small lengths with high accuracy, typically down to 0.01 mm. The screw gauge is one of the most precise simple measuring instruments available in a physics laboratory.
Core Concept
Pitch of the Screw Gauge The pitch of a screw gauge is the distance traveled by the circular scale on the linear (main) scale in one complete rotation. It is a measure of how much the spindle moves forward or backward with each full turn of the thimble.
Least Count The least count of a screw gauge is the minimum length it can measure accurately. It is found by dividing the pitch by the total number of divisions on the circular scale.
Least Count = Pitch of Screw GaugeTotal Number of Divisions on Circular Scale
Example from the text: If the pitch of the screw gauge is 0.5 mm and the number of divisions on the circular scale is 50, then: Least Count = 0.5 mm50 = 0.01 mm
- Anvil: The fixed measuring face.
- Spindle: The moving measuring face.
- Sleeve: The fixed part with the linear (main) scale.
- Thimble: The rotating part with the circular scale.
- Datum Line: The reference line on the sleeve.
- Ratchet: A mechanism to ensure consistent pressure during measurement.
- Wire piece: An object being measured.
Detailed Explanation
The screw gauge works on a simple principle: a screw can convert a small rotational motion into a small linear motion. When you rotate the thimble (the circular scale), the spindle moves along the sleeve (the linear scale). By carefully calibrating the pitch of the screw and the number of divisions on the circular scale, very small measurements can be made.
- Place the object between the anvil and the spindle and close them using the ratchet until it clicks.
- Read the main scale (linear scale) value on the sleeve, which gives the measurement in whole millimetres (or half-millimetres).
- Read the circular scale (thimble) value: find which division on the thimble aligns with the datum line on the sleeve.
- Multiply the circular scale reading by the least count.
- Add this value to the main scale reading to get the final measurement.
Total Reading = Main Scale Reading + (Circular Scale Reading × Least Count)
Zero Error in Screw Gauge The text states: "Turn the thimble until the anvil and spindle meet, datum line of the linear scale must meet with the zero on the thimble scale. If the zero mark on the thimble scale (or circular scale) does not lie directly opposite the datum line of the main scale we say that there is zero error." Like the vernier caliper, the screw gauge can have a zero error (positive or negative), which must be corrected. The correction is discussed in laboratory work.
Intermediate Level
The screw gauge is an essential instrument for precise measurements in physics and engineering. Its precision comes from the screw's ability to convert rotational motion into very small linear motion. The pitch is the key property—it is the distance the spindle moves in one full rotation. The least count is the smallest measurement the instrument can make, typically 0.01 mm. This is smaller than the least count of a vernier caliper (0.1 mm), making the screw gauge a more precise instrument. It is used to measure the thickness of wires, sheets, and other objects requiring high precision. As with any precision instrument, zero error must be checked and corrected for accurate results.
Important Points
- - A screw gauge measures lengths even smaller than a vernier caliper.
- - It works by rotating a circular scale over a linear scale.
- - The pitch is the distance the spindle moves per one rotation.
- - The least count is the smallest measurement it can make, calculated by dividing the pitch by the number of circular scale divisions.
- - A typical least count is 0.01 mm.
- - It can have a zero error that must be corrected.
Remember
- - Screw Gauge: For measurements smaller than vernier caliper.
- - Least Count: LC = PitchTotal circular divisions.
- - Typical Least Count: 0.01 mm.
- - Pitch: Distance moved per rotation.
- - Zero Error: Check if the zeros align when the anvil and spindle meet.
Common Mistakes
- - Not using the ratchet: The ratchet ensures consistent pressure. Using the thimble directly can tighten the screw too much, compressing the object and giving a wrong reading.
- - Reading the circular scale incorrectly: Make sure to look directly at the datum line when reading the circular scale to avoid parallax error.
- - Forgetting zero error: Just like the vernier caliper, you must check and correct for zero error.
Quick Revision
The screw gauge is a precision measuring instrument used to measure very small lengths, even smaller than those measured by a vernier caliper. It works by rotating a circular scale over a linear scale. The least count, which is the smallest measurement it can make, is calculated by dividing the pitch of the screw by the total number of divisions on the circular scale. A typical least count is 0.01 mm.
60-Second Revision
The screw gauge is a very precise instrument for measuring tiny lengths (e.g., wire diameter). It has a linear scale and a rotating circular scale. Its least count is calculated as PitchTotal circular divisions, typically 0.01 mm. Always use the ratchet and check for zero error.
Frequently Asked Questions (FAQs)
Q1. What is a screw gauge used for? Answer: A screw gauge (also called a micrometer) is a precision measuring instrument used to measure very small lengths, such as the thickness of a wire or the diameter of a small ball. It can measure lengths even smaller than those measured by a vernier caliper.
Q2. What is the pitch of a screw gauge? Answer: The pitch of a screw gauge is the distance traveled by the circular scale on the linear (main) scale in one complete rotation. It tells you how much the spindle moves with one full turn of the thimble.
Q3. What is the least count of a screw gauge? Answer: The least count is the minimum length that can be measured accurately with the screw gauge. It is calculated by dividing the pitch by the total number of divisions on the circular scale. A typical least count is 0.01 mm.
- Q4. How is the least count of a screw gauge calculated?
- Answer: The formula is:
- Least Count = Pitch of Screw GaugeTotal Number of Divisions on Circular Scale
- For example, if the pitch is 0.5 mm and there are 50 divisions, the least count is 0.550 = 0.01 mm.
Q5. What is zero error in a screw gauge? Answer: Zero error occurs when the zero mark on the circular scale (thimble) does not align with the datum line on the main scale when the anvil and spindle are closed. It can be positive or negative and must be corrected for accurate measurements.
Q6. What is the function of the ratchet in a screw gauge? Answer: The ratchet is a mechanism that ensures a consistent, gentle pressure is applied when tightening the screw gauge. It slips or clicks when the correct pressure is reached, preventing the user from over-tightening and compressing the object, which would lead to an incorrect reading.
Multiple Choice Questions (MCQs)
- Q1. A screw gauge is used for measurements even smaller than:
- A. A metre rule
- B. A vernier caliper
- C. A measuring tape
- D. A stopwatch
- Correct Answer: B
- Explanation: The text states that a screw gauge is used for measurements even smaller than vernier calipers.
- Q2. The distance traveled by the circular scale on the linear scale in one rotation is called the:
- A. Least count
- B. Zero error
- C. Pitch
- D. Range
- Correct Answer: C
- Explanation: The text defines pitch as the distance traveled by the circular scale on the linear (main) scale in one rotation.
- Q3. The formula for the least count of a screw gauge is:
- A. LC = Pitch × Circular divisions
- B. LC = Total circular divisionsPitch
- C. LC = PitchTotal circular divisions
- D. LC = Pitch + Total circular divisions
- Correct Answer: C
- Explanation: The text states that the least count of a screw gauge is found by dividing its pitch by the number of circular scale divisions.
- Q4. If the pitch of a screw gauge is 0.5 mm and the circular scale has 50 divisions, its least count is:
- A. 0.5 mm
- B. 0.1 mm
- C. 0.01 mm
- D. 0.001 mm
- Correct Answer: C
- Explanation: LC = 0.5 mm50 = 0.01 mm.
- Q5. Which part of the screw gauge is the fixed measuring face?
- A. Spindle
- B. Thimble
- C. Anvil
- D. Ratchet
- Correct Answer: C
- Explanation: The text's diagram (Figure 1.11) labels the anvil as the fixed part and the spindle as the moving part.
- Q6. The rotating part of the screw gauge with the circular scale is the:
- A. Sleeve
- B. Thimble
- C. Anvil
- D. Spindle
- Correct Answer: B
- Explanation: The thimble is the rotating part that contains the circular scale.
- Q7. What is the function of the ratchet on a screw gauge?
- A. To measure depth
- B. To lock the scale
- C. To ensure consistent pressure during measurement
- D. To read the main scale
- Correct Answer: C
- Explanation: The ratchet prevents over-tightening and ensures a consistent, gentle pressure is applied to the object being measured.
- Q8. The datum line is a reference line on the:
- A. Thimble
- B. Anvil
- C. Sleeve
- D. Spindle
- Correct Answer: C
- Explanation: The datum line is on the sleeve (the fixed linear scale) and is used as a reference for reading the circular scale on the thimble.
- Q9. Which instrument has a smaller least count: a vernier caliper or a screw gauge?
- A. Vernier caliper
- B. Screw gauge
- C. They have the same least count
- D. It depends on the object being measured
Correct Answer: B Explanation: The text states that the least count of a vernier caliper is 0.1 mm, while a typical screw gauge has a least count of 0.01 mm. Therefore, the screw gauge has a smaller least count.
- Q10. What is the typical least count of a screw gauge?
- A. 1 mm
- B. 0.1 mm
- C. 0.01 mm
- D. 0.001 mm
- Correct Answer: C
- Explanation: The text gives an example where the least count is calculated to be 0.01 mm, which is a typical value for a screw gauge.
Frequently Asked Questions (FAQs)
Q1. What is the difference between the pitch and the least count of a screw gauge? Answer: The pitch is the distance the spindle moves in one complete rotation of the thimble. The least count is the smallest measurement the instrument can make, which is calculated by dividing the pitch by the number of divisions on the circular scale. So, least count = pitch / circular divisions.
- Read the main scale value on the sleeve.
- Read the circular scale value on the thimble (the division that aligns with the datum line).
- Multiply the circular scale reading by the least count.
- Add this to the main scale reading. This gives the total measurement.
Q3. Why is the ratchet important in a screw gauge? Answer: The ratchet is crucial because it provides a consistent, gentle pressure when tightening the instrument. Without it, you might over-tighten the screw, compress the object being measured, and get a reading that is too small. The ratchet clicks when the correct pressure is applied, ensuring accuracy.
Q4. What is the difference between zero error in a vernier caliper and a screw gauge? Answer: The concept is similar. Zero error occurs when the instrument does not read zero when it should (jaws closed or anvil and spindle in contact). For both instruments, zero error can be positive or negative and must be determined and corrected for accurate measurements.
Q5. Can a screw gauge be used to measure the thickness of a book? Answer: No, a screw gauge is designed for very small measurements. Its range is limited, and its jaws are not wide enough to measure a book. A vernier caliper or a metre rule would be more suitable for measuring the thickness of a book.
Q6. What is the main advantage of a screw gauge over a vernier caliper? Answer: The main advantage is precision. A screw gauge has a smaller least count (typically 0.01 mm) compared to a vernier caliper (0.1 mm), so it can measure smaller lengths more accurately.
Multiple Choice Questions (MCQs)
- Q1. A screw gauge is used for measurements even smaller than:
- A. A metre rule
- B. A vernier caliper
- C. A measuring tape
- D. A stopwatch
- Correct Answer: B
- Explanation: The text states that a screw gauge is used for measurements even smaller than vernier calipers.
- Q2. The distance traveled by the circular scale on the linear scale in one rotation is called the:
- A. Least count
- B. Zero error
- C. Pitch
- D. Range
- Correct Answer: C
- Explanation: The text defines pitch as the distance traveled by the circular scale on the linear (main) scale in one rotation.
- Q3. The formula for the least count of a screw gauge is:
- A. LC = Pitch × Circular divisions
- B. LC = Total circular divisionsPitch
- C. LC = PitchTotal circular divisions
- D. LC = Pitch + Total circular divisions
- Correct Answer: C
- Explanation: The text states that the least count of a screw gauge is found by dividing its pitch by the number of circular scale divisions.
- Q4. If the pitch of a screw gauge is 0.5 mm and the circular scale has 50 divisions, its least count is:
- A. 0.5 mm
- B. 0.1 mm
- C. 0.01 mm
- D. 0.001 mm
- Correct Answer: C
- Explanation: LC = 0.5 mm50 = 0.01 mm.
- Q5. Which part of the screw gauge is the fixed measuring face?
- A. Spindle
- B. Thimble
- C. Anvil
- D. Ratchet
- Correct Answer: C
- Explanation: The text's diagram (Figure 1.11) labels the anvil as the fixed part and the spindle as the moving part.
- Q6. The rotating part of the screw gauge with the circular scale is the:
- A. Sleeve
- B. Thimble
- C. Anvil
- D. Spindle
- Correct Answer: B
- Explanation: The thimble is the rotating part that contains the circular scale.
- Q7. What is the function of the ratchet on a screw gauge?
- A. To measure depth
- B. To lock the scale
- C. To ensure consistent pressure during measurement
- D. To read the main scale
- Correct Answer: C
- Explanation: The ratchet prevents over-tightening and ensures a consistent, gentle pressure is applied to the object being measured.
- Q8. The datum line is a reference line on the:
- A. Thimble
- B. Anvil
- C. Sleeve
- D. Spindle
- Correct Answer: C
- Explanation: The datum line is on the sleeve (the fixed linear scale) and is used as a reference for reading the circular scale on the thimble.
- Q9. Which instrument has a smaller least count: a vernier caliper or a screw gauge?
- A. Vernier caliper
- B. Screw gauge
- C. They have the same least count
- D. It depends on the object being measured
Correct Answer: B Explanation: The text states that the least count of a vernier caliper is 0.1 mm, while a typical screw gauge has a least count of 0.01 mm. Therefore, the screw gauge has a smaller least count.
- Q10. What is the typical least count of a screw gauge?
- A. 1 mm
- B. 0.1 mm
- C. 0.01 mm
- D. 0.001 mm
- Correct Answer: C
- Explanation: The text gives an example where the least count is calculated to be 0.01 mm, which is a typical value for a screw gauge.
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Quick revision
Revision Zone
Review the key facts, formulas and checks before you move on.1.7.3 Screw Gauge
Sticky Notes · Quick Revision
Key Point 1
- Screw Gauge: Measures to 0.01 mm.
Key Point 2
- Least Count: PitchCircular divisions.
Key Point 3
- Pitch: Distance per rotation.
Key Point 4
- Parts: Anvil, Spindle, Sleeve, Thimble, Ratchet.
Key Point 5
- Example: Pitch = 0.5 mm, 50 divisions → LC = 0.01 mm.
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