What is the difference between a dimension and a unit? Give three examples of each.

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Answer 1

Textbook Question

Chapter 7, Problem 1CP

What is the difference between a dimension and a unit? Give three examples of each.

Expert Solution & Answer

To determine

The difference between a dimension and a unit.

Explanation of Solution

Dimension:

Dimension is defined as the measure of degree of freedom in mathematics. It is defined as the measure of physical quantity without including any numerical value. It tells us that all the independent quantities used to define the coordinates of the position or point. It falls under intrinsic property. Dimensions of complex quantity can be calculated by combining the seven-primary dimensions.

Unit:

Unit is the measurement of dimension by assigning a numerical value. It is defined as the physical quantity which gives standard value. They include numerical values to define dimensions. Unit tells a specific way to report a quantity. Units can be kept constant while doing algebraic calculations. Mathematical operations can only be performed if the dimensions of all the quantities are similar.

Sr. No.	Dimension	Unit
1	It is defined as the measure of physical quantity.	Unit is the measurement of dimension by assigning a numerical value.
2	It does not include numerical values.	They include numerical value to define dimensions.
3	Dimensions tells the nature of the quantity.	Unit tells a specific way to report a quantity.
4	Dimensions are an arbitrary chosen property (physical).	It helps in expressing dimension in numbers.
5	Examples- length, mass, time.	Examples- meter, kilogram, hour/second.

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Students have asked these similar questions

The gears shown in the figure have a diametral pitch of 2 teeth per inch and a 20° pressure angle. The pinion rotates at 1800 rev/min clockwise and transmits 200 hp through the idler pair to gear 5 on shaft c. What forces do gears 3 and 4 transmit to the idler shaft? TS I y 18T 32T This a 12 x 18T C 48T 5

Question 1. Draw 3 teeth for the following pinion and gear respectively. The teeth should be drawn near the pressure line so that the teeth from the pinion should mesh those of the gear. Drawing scale (1:1). Either a precise hand drawing or CAD drawing is acceptable. Draw all the trajectories of the involute lines and the circles. Specification: 18tooth pinion and 30tooth gear. Diameter pitch=P=6 teeth /inch. Pressure angle:20°, 1/P for addendum (a) and 1.25/P for dedendum (b). For fillet, c=b-a.

5. The figure shows a gear train. There is no friction at the bearings except for the gear tooth forces. The material of the milled gears is steel having a Brinell hardness of 170. The input shaft speed (n2) is 800 rpm. The face width and the contact angle for all gears are 1 in and 20° respectively. In this gear set, the endurance limit (Se) is 15 kpsi and nd (design factor) is 2. (a) Find the revolution speed of gear 5. (b) Determine whether each gear satisfies the design factor of 2.0 for bending fatigue. (c) Determine whether each gear satisfies the design factor of 2.0 for surface fatigue (contact stress). (d) According to the computation results of the questions (b) and (c), explain the possible failure mechanisms for each gear. N4=28 800rpm N₁=43 N5=34 N₂=14 P(diameteral pitch)=8 for all gears Coupled to 2.5hp motor

Answer 2

Textbook Question

Chapter 7, Problem 1CP

What is the difference between a dimension and a unit? Give three examples of each.

Expert Solution & Answer

To determine

The difference between a dimension and a unit.

Explanation of Solution

Dimension:

Dimension is defined as the measure of degree of freedom in mathematics. It is defined as the measure of physical quantity without including any numerical value. It tells us that all the independent quantities used to define the coordinates of the position or point. It falls under intrinsic property. Dimensions of complex quantity can be calculated by combining the seven-primary dimensions.

Unit:

Unit is the measurement of dimension by assigning a numerical value. It is defined as the physical quantity which gives standard value. They include numerical values to define dimensions. Unit tells a specific way to report a quantity. Units can be kept constant while doing algebraic calculations. Mathematical operations can only be performed if the dimensions of all the quantities are similar.

Sr. No.	Dimension	Unit
1	It is defined as the measure of physical quantity.	Unit is the measurement of dimension by assigning a numerical value.
2	It does not include numerical values.	They include numerical value to define dimensions.
3	Dimensions tells the nature of the quantity.	Unit tells a specific way to report a quantity.
4	Dimensions are an arbitrary chosen property (physical).	It helps in expressing dimension in numbers.
5	Examples- length, mass, time.	Examples- meter, kilogram, hour/second.

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Answer 3

Textbook Question

Chapter 7, Problem 1CP

What is the difference between a dimension and a unit? Give three examples of each.

Expert Solution & Answer

To determine

The difference between a dimension and a unit.

Explanation of Solution

Dimension:

Dimension is defined as the measure of degree of freedom in mathematics. It is defined as the measure of physical quantity without including any numerical value. It tells us that all the independent quantities used to define the coordinates of the position or point. It falls under intrinsic property. Dimensions of complex quantity can be calculated by combining the seven-primary dimensions.

Unit:

Unit is the measurement of dimension by assigning a numerical value. It is defined as the physical quantity which gives standard value. They include numerical values to define dimensions. Unit tells a specific way to report a quantity. Units can be kept constant while doing algebraic calculations. Mathematical operations can only be performed if the dimensions of all the quantities are similar.

Sr. No.	Dimension	Unit
1	It is defined as the measure of physical quantity.	Unit is the measurement of dimension by assigning a numerical value.
2	It does not include numerical values.	They include numerical value to define dimensions.
3	Dimensions tells the nature of the quantity.	Unit tells a specific way to report a quantity.
4	Dimensions are an arbitrary chosen property (physical).	It helps in expressing dimension in numbers.
5	Examples- length, mass, time.	Examples- meter, kilogram, hour/second.

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Answer 4

Textbook Question

Chapter 7, Problem 1CP

What is the difference between a dimension and a unit? Give three examples of each.

Expert Solution & Answer

To determine

The difference between a dimension and a unit.

Explanation of Solution

Dimension:

Dimension is defined as the measure of degree of freedom in mathematics. It is defined as the measure of physical quantity without including any numerical value. It tells us that all the independent quantities used to define the coordinates of the position or point. It falls under intrinsic property. Dimensions of complex quantity can be calculated by combining the seven-primary dimensions.

Unit:

Unit is the measurement of dimension by assigning a numerical value. It is defined as the physical quantity which gives standard value. They include numerical values to define dimensions. Unit tells a specific way to report a quantity. Units can be kept constant while doing algebraic calculations. Mathematical operations can only be performed if the dimensions of all the quantities are similar.

Sr. No.	Dimension	Unit
1	It is defined as the measure of physical quantity.	Unit is the measurement of dimension by assigning a numerical value.
2	It does not include numerical values.	They include numerical value to define dimensions.
3	Dimensions tells the nature of the quantity.	Unit tells a specific way to report a quantity.
4	Dimensions are an arbitrary chosen property (physical).	It helps in expressing dimension in numbers.
5	Examples- length, mass, time.	Examples- meter, kilogram, hour/second.

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Answer 5

Textbook Question

Answer 6

Textbook Question

Answer 7

Expert Solution & Answer

To determine

The difference between a dimension and a unit.

Explanation of Solution

Dimension:

Dimension is defined as the measure of degree of freedom in mathematics. It is defined as the measure of physical quantity without including any numerical value. It tells us that all the independent quantities used to define the coordinates of the position or point. It falls under intrinsic property. Dimensions of complex quantity can be calculated by combining the seven-primary dimensions.

Unit:

Unit is the measurement of dimension by assigning a numerical value. It is defined as the physical quantity which gives standard value. They include numerical values to define dimensions. Unit tells a specific way to report a quantity. Units can be kept constant while doing algebraic calculations. Mathematical operations can only be performed if the dimensions of all the quantities are similar.

Sr. No.	Dimension	Unit
1	It is defined as the measure of physical quantity.	Unit is the measurement of dimension by assigning a numerical value.
2	It does not include numerical values.	They include numerical value to define dimensions.
3	Dimensions tells the nature of the quantity.	Unit tells a specific way to report a quantity.
4	Dimensions are an arbitrary chosen property (physical).	It helps in expressing dimension in numbers.
5	Examples- length, mass, time.	Examples- meter, kilogram, hour/second.

Answer 8

Expert Solution & Answer

To determine

The difference between a dimension and a unit.

Explanation of Solution

Dimension:

Dimension is defined as the measure of degree of freedom in mathematics. It is defined as the measure of physical quantity without including any numerical value. It tells us that all the independent quantities used to define the coordinates of the position or point. It falls under intrinsic property. Dimensions of complex quantity can be calculated by combining the seven-primary dimensions.

Unit:

Unit is the measurement of dimension by assigning a numerical value. It is defined as the physical quantity which gives standard value. They include numerical values to define dimensions. Unit tells a specific way to report a quantity. Units can be kept constant while doing algebraic calculations. Mathematical operations can only be performed if the dimensions of all the quantities are similar.

Sr. No.	Dimension	Unit
1	It is defined as the measure of physical quantity.	Unit is the measurement of dimension by assigning a numerical value.
2	It does not include numerical values.	They include numerical value to define dimensions.
3	Dimensions tells the nature of the quantity.	Unit tells a specific way to report a quantity.
4	Dimensions are an arbitrary chosen property (physical).	It helps in expressing dimension in numbers.
5	Examples- length, mass, time.	Examples- meter, kilogram, hour/second.

Answer 9

Expert Solution & Answer

Answer 10

Expert Solution & Answer

Answer 11

To determine

The difference between a dimension and a unit.

Answer 12

Explanation of Solution

Dimension:

Dimension is defined as the measure of degree of freedom in mathematics. It is defined as the measure of physical quantity without including any numerical value. It tells us that all the independent quantities used to define the coordinates of the position or point. It falls under intrinsic property. Dimensions of complex quantity can be calculated by combining the seven-primary dimensions.

Unit:

Unit is the measurement of dimension by assigning a numerical value. It is defined as the physical quantity which gives standard value. They include numerical values to define dimensions. Unit tells a specific way to report a quantity. Units can be kept constant while doing algebraic calculations. Mathematical operations can only be performed if the dimensions of all the quantities are similar.

Sr. No.	Dimension	Unit
1	It is defined as the measure of physical quantity.	Unit is the measurement of dimension by assigning a numerical value.
2	It does not include numerical values.	They include numerical value to define dimensions.
3	Dimensions tells the nature of the quantity.	Unit tells a specific way to report a quantity.
4	Dimensions are an arbitrary chosen property (physical).	It helps in expressing dimension in numbers.
5	Examples- length, mass, time.	Examples- meter, kilogram, hour/second.

Answer 13

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What is the difference between a dimension and a unit? Give three examples of each.

Solution Summary: The author explains the difference between dimension and unit. Dimension is defined as the measure of degree of freedom in mathematics.

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