Dynamics quiz questions

The number of coordinates required to specify the positions of all parts of a system having two degrees of freedom is:

2

At most, for constrained plane motion the maximum number of available equations available to solve for unknowns is

5

Spherical coordinates use coordinates that consist of:

A radial distance and two angles.

The position of a particle, A, with respect to a particle, B, can be expressed as rA/B = rA - rB where the subscript notation A/B means:

A with respect to B

The slope of the velocity versus time curve is the:

Acceleration

For a particle in plane curvilinear motion in a circle of constant radius, r, the direction of the component of acceleration, v2/r is:

Along the radial direction toward the center of the circle.

The moment of linear momentum is the:

Angular momentum.

The displacement divided by the time interval is the:

Average velocity

For an object in straight-line motion that has a negative velocity, the acceleration would be positive if the velocity:

Becomes less negative.

Work is defined as the:

Dot product of force with a differential displacement.

The parallel axis theorem is used to

Express the moment of inertia of a body about an axis that is parallel to an axis through the mass center of the body.

The vector symbol used for linear momentum in dynamics is:

G

The vector symbol used for angular momentum in dynamics is:

H

The angular momentum Ho of a particle of mass m moving with a velocity v with a position vector r with respect to origin o is calculated as

H0=r x mv

Select the one true statement from the four choices offered below:

If the resultant moment about a fixed point is zero, then the angular momentum about that point is conserved.

The integration of the equation of motion with respect to time rather than displacement leads to equations of:

Impulse and momentum.

Angular momentum:

Is calculated as the moment of linear momentum.

In the expression for kinetic energy for a mass system, T=(1/2)mv¯2+Σ(1/2)mi|vi|2 the second term represents the:

Kinetic energy due to motion of all particles relative to the mass-center.

In the case of the direct central impact of two spheres in collinear motion that collide with each other in an elastic impact:

Linear momentum and kinetic energy are both conserved.

The product of mass with velocity is the:

Linear momentum.

The coefficient of restitution for an impact between two particles is the ratio of the:

Magnitude of the restoration impulse to the magnitude of the deformation impulse.

Newton's second law relates force to:

Mass and acceleration.

For particles moving along a plane curvilinear path, analysis of motion:

May use normal and tangential coordinates, polar coordinates, or rectangular coordinates.

Kinematics is the branch of dynamics which describes the:

Motion of bodies without reference to the forces which either cause the motion or are generated as a result of the motion.

For a rigid body:

No net work is done by the internal interacting forces.

For a couple M acting on a body, the power developed by the couple is given by

P = Mω.

The velocity vA/B represents the velocity of:

Point A with respect to point B.

A solid system of particles wherein the distances between particles remain essentially unchanged is called a:

Rigid body.

The magnitude of the velocity is the:

Speed

For a rigid body rotating with angular velocity ω about a fixed axis through point O the kinetic energy is

T= (1/2) IO ω^2

The notation aB/A denotes

The acceleration of point B relative to point A.

Consideration of rectilinear motion of an object can be simplified by treating the motion of the body as that of a particle if:

The analysis is concerned only with the motion of the center of mass.

Impact refers to:

The collision between two bodies.

In the expression of Newton's second law for a system of constant mass, Σ⁢F=ma¯:

The force term can be calculated by considering only the external forces.

The inertia of a particle is:

The particle's resistance to rate of change of velocity.

Linear momentum is conserved if:

The resultant external force acting on the mass system is zero.

A necessary condition for conservation of angular momentum of a particle is:

The resultant moment about a fixed point of all the forces acting on the particle must be zero.

The equation Σ⁢M0=H0˙ for a general mass system states that the sum of the moments of all external forces about a fixed point is equal to:

The time rate of change of the angular momentum about that point.

U1-2

The work done on the system during an interval of motion by all non-conservative forces.

A necessary condition for the conservation of angular momentum for a general mass system is that:

There is no angular impulse about a fixed point (or about the mass center).

A particle that is free to move in space has:

Three degrees of freedom.

Space curvilinear motion can be completely specified by using:

Three independent coordinates.

The equation Σ⁢F=mv¯˙ for a system of particles states that the sum of the external forces acting on a system of particles is equal to the:

Time rate of change of the momentum of the system, assuming mass is constant in the system.

The elastic potential energy of a spring Ve depends on the spring constant k of the spring and the extension of the spring according to:

Ve=1/2kx^2

The slope of the displacement versus time curve is the:

Velocity

The mass moment of inertia, I, about a particular axis is

a measure of the resistance to change in rotational velocity.

Kinetic energy of a particle is:

a scalar quantity

In the description of plane curvilinear motion using coordinates n normal to the path and t tangent to the path of motion with unit vector en in the n- direction and the unit vector et in the t direction, the acceleration can be expressed in terms of velocity, v, the radius of curvature of the curvilinear path, ρ and the time derivative of the velocity, as:

a=(v^2/p)*en+v dot*et

In the case of a particle in uniform circular motion in a circle of radius, r, at speed, v, the acceleration, a, is:

a=v^2/r

For a rigid body in general plane motion the instantaneous center of zero velocity is a point

about which the object may be considered to be in pure rotation.

For rotation about a fixed axis the normal component of acceleration that is directed toward the axis of rotation is expressed in terms of the angular velocity ω and the vector r directed from the axis of rotation to the point of interest as

an = ω × (ω ×r).

For rotation about a fixed axis the component of acceleration that is directed tangent to the curve of the motion at is calculated as

at = α × r.

For purely translational motion

at all times every line in a body remains parallel to its original orientation.

For purely translational motion

at all times every line in a body remains parallel to its original position.

The instantaneous acceleration of a particle can be calculated as:

dv/dt

A defined mass of liquid or gaseous particles flowing at a specified rate is an example of a:

nonrigid body

When a rigid body rotates about a fixed axis all points

other than those on the axis move in concentric circles about the fixed axis.

For two points on the same rigid body that is in rotational motion the relative linear velocity of one point with respect to the other is always

perpendicular to the line joining the two points in question.

The time rate of doing work is the:

power

Angular momentum of a particle about a point is expressed in terms of the mass of a particle, m, the velocity of the particle, v, and the vector from the pivot point to a point on the line of action of the velocity vector, r is:

r x(mv)

The tangential component of the relative acceleration due to rotation, (aA/B)t is

r α.

When using cylindrical coordinates for space curvilinear motion the coordinates used are:

r, θ, z.

The kinetics of rigid bodies deals with

relating the action of forces on bodies to their resulting translational and rotational motions of the body.

The equation ΣMG=H˙G states that the

resultant moment about the mass center of the external forces on the body equals the time rate of change of the angular momentum of the body about its center of mass.

The normal component of the relative acceleration due to rotation, (aA/B)n is

rw^2

The magnitude of the velocity vector is called the:

speed and it is a scalor

The equation ΣF = m ā states that the

sum of the external forces acting on a body is equal to the mass of the body times the acceleration of the mass center of the body.

A system of particles may be considered to be a rigid body if

the distances between the particles remain unchanged

In absolute-motion analysis, if the angular position of a moving line in the plane of motion is specified by its counterclockwise angle measured from some fixed reference axis then _______

the positive sense for angular velocity is counterclockwise and the positive sense for angular acceleration is also counterclockwise.

For rotation of a rigid body, all lines on the rigid body in its plane of motion have

the same angular displacement, the same angular velocity, and the same angular acceleration.

The equation ΣMG = I α expresses the relationship between

the summation of moments and the angular acceleration.

The approach of using absolute motion involves finding the velocities and accelerations of an object by taking the time derivatives of the defining geometric relations used to describe the configuration of the object.

true

For rotation about a fixed axis, the relationship between the velocity, v, the vector between the axis and point of interest, r, and the angular velocity, ω, is

v = ω × r.

For plane curvilinear motion with the displacement, r, expressed in polar coordinates as r = r er where er is the unit vector in the outward radial direction and eθ is the vector normal to the radial direction, the velocity is given as:

v=r dot *er+r*pheta dot*epheta

In the case of a particle in circular motion the tangential component of velocity along the circular path is calculated as:

v=r pheta single dot

In using polar coordinates to describe plane polar motion the velocity is expressed as:

v=rdot*er+r*phetadot*epheta

When using cylindrical coordinates for space curvilinear motion the expression for velocity is:

v=rdot*er+r*phetadot*epheta+zk

The velocity of point A with respect to point B is expressed in terms of the angular-velocity vector ω and the vector rA/B from point A to point B is calculated as

vA/B = ω × r

Acceleration, a, velocity, v, and displacement, s, can be related to each other without the use of time as:

vdv=ads

The time derivative of a vector is a:

vector