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

Question

Want to see more full solutions like this?

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.

Want to see more full solutions like this?

Subscribe now to access step-by-step solutions to millions of textbook problems written by subject matter experts!

Students have asked these similar questions

Two springs and two masses are attached in a straight vertical line as shown in Figure Q3. The system is set in motion by holding the mass m₂ at its equilibrium position and pushing the mass m₁ downwards of its equilibrium position a distance 2 m and then releasing both masses. if m₁ = m₂ = 1 kg, k₁ = 3 N/m and k₂ = 2 N/m. www.m k₁ = 3 (y₁ = 0). m₁ = 1 k2=2 (y₂ = 0) |m₂ = 1 Y2 y 2 System in static equilibrium (Net change in spring length =32-31) System in motion Figure Q3 - Coupled mass-spring system Determine the equations of motion y₁(t) and y₂(t) for the two masses m₁ and m₂ respectively: Analytically (hand calculations)

100 As a spring is heated, its spring constant decreases. Suppose the spring is heated and then cooled so that the spring constant at time t is k(t) = t sin N/m. If the mass-spring system has mass m = 2 kg and a damping constant b = 1 N-sec/m with initial conditions x(0) = 6 m and x'(0) = -5 m/sec and it is subjected to the harmonic external force f(t) = 100 cos 3t N. Find at least the first four nonzero terms in a power series expansion about t = 0, i.e. Maclaurin series expansion, for the displacement: Analytically (hand calculations)

this is answer to a vibrations question. in the last part it states an assumption of x2, im not sure where this assumption comes from. an answer would be greatly appreciated

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.

Want to see more full solutions like this?

Subscribe now to access step-by-step solutions to millions of textbook problems written by subject matter experts!

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.

Want to see more full solutions like this?

Subscribe now to access step-by-step solutions to millions of textbook problems written by subject matter experts!

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.

Want to see more full solutions like this?

Subscribe now to access step-by-step solutions to millions of textbook problems written by subject matter experts!

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

Ch. 7 - What is the difference between a dimension and a...Ch. 7 - List the seven primary dimensions. What is...Ch. 7 - Write the primary dimensions of the universal...Ch. 7 - Write the primary dimensions of each of the...Ch. 7 - Prob. 5P Ch. 7 - Prob. 6P Ch. 7 - Prob. 7P Ch. 7 - On a periodic chart of the elements, molar mass...Ch. 7 - Prob. 9P Ch. 7 - The moment of force(M)is formed by the cross...

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.

Videos

Explanation of Solution

Want to see more full solutions like this?

Chapter 7 Solutions