The SI unit radian and explain when it is appropriate to include and when the unit should be dropped.

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Answer 1

Question

Definition Definition Rate of change of angular velocity. Angular acceleration indicates how fast the angular velocity changes over time. It is a vector quantity and has both magnitude and direction. Magnitude is represented by the length of the vector and direction is represented by the right-hand thumb rule. An angular acceleration vector will be always perpendicular to the plane of rotation. Angular acceleration is generally denoted by the Greek letter α and its SI unit is rad/s 2 .

Chapter 8, Problem 1QAP

To determine

To Define:

The SI unit radian and explain when it is appropriate to include and when the unit should be dropped.

Expert Solution & Answer

Explanation of Solution

Introduction:

A unit of measurement of angles equal to approximately 57.3 °, equivalent to the angle subdued at the center of a circle by an arc equal to the radius in length.

The relationship between speed and radius of the rotation of an object can be rewritten as v= rω or ω=vr

A distance r from the point of rotation moving at v for an object or piece of an object. Since angular velocity v is the same for any rotating object element, the above equation tells us that the velocity of any rotating object element increases at the same rate as the distance r from the rotating point increases.

In measuring certain rotational speeds, we use "rotations per minute "not "degrees per second ".

When a satellite orbits the Earth, we see its speed in "miles per hour "rather than" degrees per hour". Now divide by the distance to the satellite and the orbital speed is achieved in radians per hour.

Angular acceleration is measured in radians per second per second.

The radian is a dimensionless unit that may be dropped, although the plane-angle is not an official measure (SI) and radian can be dropped.

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Answer 2

Question

Definition Definition Rate of change of angular velocity. Angular acceleration indicates how fast the angular velocity changes over time. It is a vector quantity and has both magnitude and direction. Magnitude is represented by the length of the vector and direction is represented by the right-hand thumb rule. An angular acceleration vector will be always perpendicular to the plane of rotation. Angular acceleration is generally denoted by the Greek letter α and its SI unit is rad/s 2 .

Chapter 8, Problem 1QAP

To determine

To Define:

The SI unit radian and explain when it is appropriate to include and when the unit should be dropped.

Expert Solution & Answer

Explanation of Solution

Introduction:

A unit of measurement of angles equal to approximately 57.3 °, equivalent to the angle subdued at the center of a circle by an arc equal to the radius in length.

The relationship between speed and radius of the rotation of an object can be rewritten as v= rω or ω=vr

A distance r from the point of rotation moving at v for an object or piece of an object. Since angular velocity v is the same for any rotating object element, the above equation tells us that the velocity of any rotating object element increases at the same rate as the distance r from the rotating point increases.

In measuring certain rotational speeds, we use "rotations per minute "not "degrees per second ".

When a satellite orbits the Earth, we see its speed in "miles per hour "rather than" degrees per hour". Now divide by the distance to the satellite and the orbital speed is achieved in radians per hour.

Angular acceleration is measured in radians per second per second.

The radian is a dimensionless unit that may be dropped, although the plane-angle is not an official measure (SI) and radian can be dropped.

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Answer 3

Question

Definition Definition Rate of change of angular velocity. Angular acceleration indicates how fast the angular velocity changes over time. It is a vector quantity and has both magnitude and direction. Magnitude is represented by the length of the vector and direction is represented by the right-hand thumb rule. An angular acceleration vector will be always perpendicular to the plane of rotation. Angular acceleration is generally denoted by the Greek letter α and its SI unit is rad/s 2 .

Chapter 8, Problem 1QAP

To determine

To Define:

The SI unit radian and explain when it is appropriate to include and when the unit should be dropped.

Expert Solution & Answer

Explanation of Solution

Introduction:

A unit of measurement of angles equal to approximately 57.3 °, equivalent to the angle subdued at the center of a circle by an arc equal to the radius in length.

The relationship between speed and radius of the rotation of an object can be rewritten as v= rω or ω=vr

A distance r from the point of rotation moving at v for an object or piece of an object. Since angular velocity v is the same for any rotating object element, the above equation tells us that the velocity of any rotating object element increases at the same rate as the distance r from the rotating point increases.

In measuring certain rotational speeds, we use "rotations per minute "not "degrees per second ".

When a satellite orbits the Earth, we see its speed in "miles per hour "rather than" degrees per hour". Now divide by the distance to the satellite and the orbital speed is achieved in radians per hour.

Angular acceleration is measured in radians per second per second.

The radian is a dimensionless unit that may be dropped, although the plane-angle is not an official measure (SI) and radian can be dropped.

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Answer 4

Question

Definition Definition Rate of change of angular velocity. Angular acceleration indicates how fast the angular velocity changes over time. It is a vector quantity and has both magnitude and direction. Magnitude is represented by the length of the vector and direction is represented by the right-hand thumb rule. An angular acceleration vector will be always perpendicular to the plane of rotation. Angular acceleration is generally denoted by the Greek letter α and its SI unit is rad/s 2 .

Chapter 8, Problem 1QAP

To determine

To Define:

The SI unit radian and explain when it is appropriate to include and when the unit should be dropped.

Expert Solution & Answer

Explanation of Solution

Introduction:

A unit of measurement of angles equal to approximately 57.3 °, equivalent to the angle subdued at the center of a circle by an arc equal to the radius in length.

The relationship between speed and radius of the rotation of an object can be rewritten as v= rω or ω=vr

A distance r from the point of rotation moving at v for an object or piece of an object. Since angular velocity v is the same for any rotating object element, the above equation tells us that the velocity of any rotating object element increases at the same rate as the distance r from the rotating point increases.

In measuring certain rotational speeds, we use "rotations per minute "not "degrees per second ".

When a satellite orbits the Earth, we see its speed in "miles per hour "rather than" degrees per hour". Now divide by the distance to the satellite and the orbital speed is achieved in radians per hour.

Angular acceleration is measured in radians per second per second.

The radian is a dimensionless unit that may be dropped, although the plane-angle is not an official measure (SI) and radian can be dropped.

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Answer 5

Chapter 8, Problem 1QAP

To determine

To Define:

The SI unit radian and explain when it is appropriate to include and when the unit should be dropped.

Expert Solution & Answer

Explanation of Solution

Introduction:

A unit of measurement of angles equal to approximately 57.3 °, equivalent to the angle subdued at the center of a circle by an arc equal to the radius in length.

The relationship between speed and radius of the rotation of an object can be rewritten as v= rω or ω=vr

A distance r from the point of rotation moving at v for an object or piece of an object. Since angular velocity v is the same for any rotating object element, the above equation tells us that the velocity of any rotating object element increases at the same rate as the distance r from the rotating point increases.

In measuring certain rotational speeds, we use "rotations per minute "not "degrees per second ".

When a satellite orbits the Earth, we see its speed in "miles per hour "rather than" degrees per hour". Now divide by the distance to the satellite and the orbital speed is achieved in radians per hour.

Angular acceleration is measured in radians per second per second.

The radian is a dimensionless unit that may be dropped, although the plane-angle is not an official measure (SI) and radian can be dropped.

Answer 6

Chapter 8, Problem 1QAP

To determine

To Define:

The SI unit radian and explain when it is appropriate to include and when the unit should be dropped.

Expert Solution & Answer

Explanation of Solution

Introduction:

A unit of measurement of angles equal to approximately 57.3 °, equivalent to the angle subdued at the center of a circle by an arc equal to the radius in length.

The relationship between speed and radius of the rotation of an object can be rewritten as v= rω or ω=vr

A distance r from the point of rotation moving at v for an object or piece of an object. Since angular velocity v is the same for any rotating object element, the above equation tells us that the velocity of any rotating object element increases at the same rate as the distance r from the rotating point increases.

In measuring certain rotational speeds, we use "rotations per minute "not "degrees per second ".

When a satellite orbits the Earth, we see its speed in "miles per hour "rather than" degrees per hour". Now divide by the distance to the satellite and the orbital speed is achieved in radians per hour.

Angular acceleration is measured in radians per second per second.

The radian is a dimensionless unit that may be dropped, although the plane-angle is not an official measure (SI) and radian can be dropped.

Answer 7

Chapter 8, Problem 1QAP

To determine

To Define:

The SI unit radian and explain when it is appropriate to include and when the unit should be dropped.

Answer 8

Expert Solution & Answer

Explanation of Solution

Introduction:

A unit of measurement of angles equal to approximately 57.3 °, equivalent to the angle subdued at the center of a circle by an arc equal to the radius in length.

The relationship between speed and radius of the rotation of an object can be rewritten as v= rω or ω=vr

A distance r from the point of rotation moving at v for an object or piece of an object. Since angular velocity v is the same for any rotating object element, the above equation tells us that the velocity of any rotating object element increases at the same rate as the distance r from the rotating point increases.

In measuring certain rotational speeds, we use "rotations per minute "not "degrees per second ".

When a satellite orbits the Earth, we see its speed in "miles per hour "rather than" degrees per hour". Now divide by the distance to the satellite and the orbital speed is achieved in radians per hour.

Angular acceleration is measured in radians per second per second.

The radian is a dimensionless unit that may be dropped, although the plane-angle is not an official measure (SI) and radian can be dropped.

Answer 9

Expert Solution & Answer

Answer 10

Expert Solution & Answer

Answer 11

Ch. 8 - Prob. 1QAP Ch. 8 - Prob. 2QAP Ch. 8 - Prob. 3QAP Ch. 8 - Prob. 4QAP Ch. 8 - Prob. 5QAP Ch. 8 - Prob. 6QAP Ch. 8 - Prob. 7QAP Ch. 8 - Prob. 8QAP Ch. 8 - Prob. 9QAP Ch. 8 - Prob. 10QAP

The SI unit radian and explain when it is appropriate to include and when the unit should be dropped.

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To Define:

The SI unit radian and explain when it is appropriate to include and when the unit should be dropped.

Explanation of Solution

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Chapter 8 Solutions

The SI unit radian and explain when it is appropriate to include and when the unit should be dropped.

Concept explainers

Videos

To Define: The SI unit radian and explain when it is appropriate to include and when the unit should be dropped.

Explanation of Solution

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Chapter 8 Solutions

To Define:

The SI unit radian and explain when it is appropriate to include and when the unit should be dropped.