Conceptual and Mathematical Basics
Conceptual and Mathematical Basics

Conceptual and Mathematical Basics

Lead Author(s): Saylor Academy

Source: Saylor

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A question pack on dynamics in mechanical engineering.

This content is licensed under the Creative Commons Attribution 3.0 Unported License.

Conceptual and Mathematical Basics Q1

Acceleration is the first derivative of which of the following?

A

Time

B

Distance

C

Velocity

D

None of the above

Conceptual and Mathematical Basics Q2

Cylindrical coordinates comprise which of the following vectors?

A

Position

B

Acceleration

C

Velocity

D

All of the above

Conceptual and Mathematical Basics Q3

Distance is the integral of which of the following?

A

Time

B

Velocity

C

Acceleration

D

None of the above

Conceptual and Mathematical Basics Q4

The absolute position of two particles is measured with respect to the origin of which of the following frames of motion?

A

Fixed frame

B

Moving frame

C

Both A and B

D

None of the above

Conceptual and Mathematical Basics Q5

Velocity is the integral of which of the following?

A

Time

B

Distance

C

Acceleration

D

None of the above

Conceptual and Mathematical Basics Q6

Which of the following components are used to define the position of a particle in one‑dimension using polar coordinates?

A

Radial coordinates

B

Traverse coordinates

C

Both A and B

D

None of the above

Conceptual and Mathematical Basics Q8

Velocity is the first derivative of which of the following?

A

Time

B

Distance

C

Acceleration

D

None of the above

Conceptual and Mathematical Basics Q7

Equations of motion in cylindrical coordinates involve how many components?

A

1

B

2

C

3

D

4

Conceptual and Mathematical Basics Q10

Newton’s “Second” law is also known as which of the following?

A

Law of inertia

B

Law of force

C

Law of action‑reaction

D

Law of gravitational attraction

Conceptual and Mathematical Basics Q9

Newton’s “Third” law is also known as which of the following?

A

Law of inertia

B

Law of force

C

Law of action‑reaction

D

Law of gravitational attraction

Conceptual and Mathematical Basics Q11

Which of the following best describes what Newton’s 3rd law states?

A

Newton’s 3rd law states that each action has a reaction equal in magnitude.

B

Newton’s 3rd law states that each action has a reaction opposite in direction.

C

Both A and B

D

None of the above

Conceptual and Mathematical Basics Q12

Newton’s “First” law is also known as which of the following?

A

Law of inertia

B

Law of force

C

Law of action‑reaction

D

Law of gravitational attraction

Conceptual and Mathematical Basics Q17

Impulses caused at the connections of system of rigid particles are ______________.

A

Internal

B

External

C

Both internal and external

D

Neither internal nor external

Conceptual and Mathematical Basics Q13

Moment of Inertia (I) generally involves ______________ integral.

A

Single

B

Double

C

Triple

D

Quadruple

Conceptual and Mathematical Basics Q14

Radius of gyration is the square root of ______________.

A

Moment of Inertia (I) divided by mass (m).

B

Moment of Inertia (I) divided by force (N).

C

Moment of Inertia (I) divided by displacement.

D

None of the above

Conceptual and Mathematical Basics Q16

In solids of revolution which of the following is true?

A

x‑y plane rotates about x axis.

B

x‑y plane rotates about z axis.

C

y‑z plane rotates about z axis.

D

y‑z plane rotates about y axis.

Conceptual and Mathematical Basics Q19

In US customary units, what is the standard unit Moment of Inertia (I)?

A

(Kg) (m2^2)

B

(Slug) (ft2^2)

C

(N) (m2^2)

D

(lb) (ft2^2)

Conceptual and Mathematical Basics Q18

Kinetic energy of a two‑dimensional rigid body is zero under which circumstance?

A

Body rotating about a pin support

B

Wheel rotating without slipping

C

Force acts perpendicular in direction of displacement

D

All of the above

Conceptual and Mathematical Basics Q20

Moment of Inertia (I) is equivalent to which of the following in linear motion?

A

Acceleration

B

Momentum

C

Impulse

D

Mass

Conceptual and Mathematical Basics Q21

Moment of Inertia (I) is integral for which of the following?

A

First moment of mass

B

Second moment of mass

C

Both A and B

D

None of the above

Conceptual and Mathematical Basics Q22

The center of mass generally describes which of the following?

A

Circular path

B

Linear path

C

Both A and B

D

None of the above

Conceptual and Mathematical Basics Q23

The equation of motion for two‑dimensional rigid body is applied to which of the following?

A

Center of gravity

B

Center of mass

C

Origin

D

None of the above

Conceptual and Mathematical Basics Q24

Which of the following is true of Moment of Inertia (I)?

A

It is a positive quantity.

B

It is a negative quantity.

C

Both A and B

D

None of the above

Conceptual and Mathematical Basics Q25

Which of the following methods can be used to compute Moment of Inertia (I)?

A

Shell method

B

Disk method

C

Volume method

D

All of the above

Conceptual and Mathematical Basics Q26

Moment of Inertia (I) is applied to bodies undergoing which type of acceleration?

A

Linear acceleration

B

Angular acceleration

C

Both A and B

D

None of the abov

Conceptual and Mathematical Basics Q27

In three‑dimensions, which of the following is true of the product of inertia?

A

The product of inertia can be a negative quantity.

B

The product of inertia can be a positive quantity.

C

The product of inertia can be zero.

D

All of the above

Conceptual and Mathematical Basics Q28

The position of a body in three‑dimensions is comprised of how many components?

A

1

B

3

C

6

D

9

Conceptual and Mathematical Basics Q29

Which of the following are examples of space curves in three‑dimensions?

A

Body cone

B

Space cone

C

Both A and B

D

None of the above

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