Rigid-Body Dynamics HW Reading Questions

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: Ho = (1/2)r x mv Ho = r x mv Ho = mv x r Ho = r * mv

Ho = r x mv

The statement that the acceleration of a particle is proportional to the resultant force acting on it and is in the direction of this force is Newton's: Second law. Third law. Fourth law. First law.

Second law.

In the Work-Energy Equation for a rigid body, T1 + V1 + U1-2 = T2 + V2, U1-2 is: The gravitational work done on the object. The change in potential energy of the object. The work done by the object. The work done on the system during an interval of motion by all non-conservative forces.

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

The tangential component of the relative acceleration due to rotation, (aA/B)t is r ω. r v. r ω2 . r α.

r α.

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 ω = v × r. v = (ω · r)r. v = ω × r. v = r × ω.

v = ω × r.

The Coriolis acceleration is expressed as ω × vrel. 2 ω × vrel. 2 vrel × ω. vrel × ω.

2 ω × vrel.

The sea-level value for the acceleration of gravity at 45 deg latitude is: 9.81 m/s2. 32.2 m/s2. 32.2 ft/s. 9.8 ft/s2.

9.81 m/s2.

Kinetic energy of a particle is: A vector quantity for which the direction is that of the velocity of the particle. A scalar quantity. Directly proportional to the velocity of the particle. A positive quantity if the velocity is in the positive direction and negative if the velocity is in the negative direction.

A scalar quantity.

The slope of the velocity versus time curve is the: Inverse of the acceleration. Acceleration. Work done. Displacement.

Acceleration.

The moment of linear momentum is the: Angular impulse. Kinetic energy Linear impulse. Angular momentum.

Angular momentum.

The displacement divided by the time interval is the: Average acceleration. Force. Momentum. Average velocity.

Average velocity.

For an object in straight-line motion that has a negative velocity, the acceleration would be positive if the velocity: Does not change. Becomes less negative. Becomes more negative.

Becomes less negative.

The quantities mass, length, and time are : Units. Dimensions. Dimensions or units depending upon the system of units employed. Both dimensions and units.

Dimensions.

Work is defined as the: Dot product of force with velocity. Dot product of force with a differential displacement. Cross product of force with velocity. Cross product of force with a differential displacement

Dot product of force with a differential displacement.

The instantaneous center of zero velocity is fixed in space. True False

False

The instantaneous center of zero velocity is momentarily at rest and its acceleration is also always zero. True False

False

The vector symbol used for linear momentum in dynamics is: H I M G

G

The vector symbol used for angular momentum in dynamics is: H M I G

H

The integration of the equation of motion with respect to time rather than displacement leads to equations of: Power Potential energy. Kinetic energy. Impulse and momentum.

Impulse and momentum.

The part of dynamics which relates the action of forces on bodies to their resulting motions is: Kinetics. Energetics. Kinematics. Statics.

Kinetics.

Kinematics is the branch of dynamics which describes the: Motion of bodies and the forces that are generated as a result of the motion. Motion of bodies without reference to the forces which either cause the motion or are generated as a result of the motion. Forces that cause motion without regard to the nature of the motion. Motion of bodies and the forces which cause the motion.

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

For a couple M acting on a body, the power developed by the couple is given by P = Mv. P = Mv2. P = Mω. P = M (dv/dt).

P = Mω.

In dynamics a body for which the dimensions are negligible is called a: Mass. Vector. Rigid body. Particle.

Particle.

A solid system of particles wherein the distances between particles remain essentially unchanged is called a: Fixed body. Stationary body. Flexible body. Rigid body.

Rigid body.

Mass is a: Vector. Scalar.

Scalar.

For the case of general plane motion, the kinetic energy is calculated as T = (1/2) m (vG^2) + (1/2) m ω^2. T = (1/2) m(vG^2) + (1/2) IG a^2. T = (1/2) m (vG^2) + (1/2) IG ω^2. T = (1/2) IG (vG^2) + (1/2) IG ω^2.

T = (1/2) m vG2 + (1/2) IG ω2.

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. T= (1/2) Io v^2. T= (1/2) Io ω^2. T= (1/2) Io v.

T= (1/2) Io ω^2.

Impact refers to: Any action of a force on a particle. The motion of a particle under the influence of a central force. A force producing a moment on a body about a fixed point. The collision between two bodies.

The collision between two bodies.

In the expression of Newton's second law for a system of constant mass, Σ⁢F=ma¯: The acceleration term represents the acceleration of a particle located at the center of mass. The internal forces must be considered when calculating the force term. The force term can be calculated by considering only the external forces. The vector representing the net force must pass through the center of mass of the system.

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

The equation Σ⁢Mo=Ho˙ for a general mass system states that the sum of the moments of all external forces about a fixed point is equal to: The total linear momentum of the system. The total angular momentum of the system about that point. The time rate of change of the linear momentum of the system. The time rate of change of the angular momentum about that point.

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

A particle that is free to move in space has: Four degrees of freedom. One degree of freedom. Two degrees of freedom. Three degrees of freedom.

Three degrees of freedom.

Space curvilinear motion can be completely specified by using: Two independent coordinates. Two independent coordinates plus a third coordinate dependent upon one of the independent coordinates. Three independent coordinates. One coordinate along the radial direction between the origin and the location of the particle.

Three independent coordinates.

During a finite rotation, the work done by a couple M which is perpendicular to the plane of motion is U=∫Fⅆθ. U=∫Mⅆθ. U=∫M⁢ωⅆθ. U=∫F⁢ωⅆθ.

U=∫Mⅆθ.

Force is a: Vector. Scalar.

Vector.

In the case of a particle in uniform circular motion in a circle of radius, r, at speed, v, the acceleration, a, is: a = r v^2. a = v^2/r. a = r v. a = r^2v.

a = v^2/r.

The mass moment of inertia, I, about a particular axis is the resistance of a rigid body to linear motion produced by a force. independent of the mass of a rigid body. a measure of the resistance to change in rotational velocity. independent of the radial distribution of mass around a particular axis.

a measure of the resistance to change in rotational velocity.

For the case of rotation of a rigid body about a fixed axis through its mass center the net external moment acting on the object must be zero. net external force acting on the object is not zero. acceleration of the center of mass of the body is zero. angular acceleration of the body is zero.

acceleration of the center of mass of the body is zero.

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 ×r. an = (ω ×r) × ω. an = r × (ω ×r). an = ω × (ω ×r).

an = ω × (ω ×r).

The time derivative of the unit vector, j, can be calculated as dj/dt = j × ω. dj/dt = j · ω. dj/dt = ω × j .

dj/dt = ω × j .

The instantaneous acceleration of a particle can be calculated as: ds/dt. v dt. d2v /dt2. dv/dt.

dv/dt.

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 parallel to the line joining the two points in question. perpendicular to the line joining the two points in question.

perpendicular to the line joining the two points in question.

For linear momentum to be conserved kinetic energy must also be conserved. the net external linear impulse acting on the system must be zero. potential energy must also be conserved. angular momentum must also be conserved.

the net external linear impulse acting on the system must be zero.

The equation ΣMG = I α expresses the relationship between the summation of moments and the linear acceleration. the summation of moments and the angular acceleration. the summation of moments and the angular velocity. the summation of forces and the linear acceleration.

the summation of moments and the angular acceleration.

Angular momentum of a body is conserved if the kinetic energy is constant. the linear momentum is conserved. there is no resultant linear impulse on the body. there is no resultant angular impulse on the body.

there is no resultant angular impulse on the body.

The linear momentum vector undergoes no change if there is no resultant linear impulse. there is no resultant angular impulse. the kinetic energy is constant. the angular momentum is conserved.

there is no resultant linear impulse.

Acceleration, a, velocity, v, and displacement, s, can be related to each other without the use of time as: v dv = a ds. v = a d2/ds2. a dv = v ds. a = v d2v/ds2.

v dv = a ds

In using polar coordinates to describe plane polar motion the velocity is expressed as: v= r˙ er+r θ˙ eθ v=r θ˙ er+ r˙ θ eθ v=r θ˙ er+ r˙ eθ v= r˙ θ er+r θ˙ eθ

v= r˙ er+r θ˙ eθ

In the case of a particle in circular motion the tangential component of velocity along the circular path is calculated as: v=r θ˙ v=r2 θ v=r θ¨ v=r θ˙2

v=r θ˙

When using cylindrical coordinates for space curvilinear motion the expression for velocity is: v=r˙ er+r θ˙ eθ+r ˙k v=r˙ er+r eθ+z ˙k v=r˙ er+r θ˙ eθ+z ˙k v=r˙ er+r θ eθ+z ˙k

v=r˙ er+r θ˙ eθ+z ˙k

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˙eθ+rθ˙er v=r˙ er-rθ˙eθ v=r˙er+r θeθ v=r˙er+rθ˙eθ

v=r˙er+rθ˙eθ

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 = r . ω. vA/B = ω × r vA/B = (∂rA/B/∂t) vA/B = ω × (∂rA/B/∂t)

vA/B = ω × r

The mass of a body is: Inversely proportional to the resistance of the body to a change in its motion. Dependent upon how far the body is from the center of the Earth. A quantitative measure of the inertia of the body. Equivalent to its weight.

A quantitative measure of the inertia of the body.

Spherical coordinates use coordinates that consist of: A radial distance and two angles. The distance along the path and two angles. A radial distance and three angles. A radial distance and an angle in a plane plus an axis perpendicular to the plane.

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 vector from the origin to particle B. The vector from the origin to particle A. B with respect to A.

A with respect to B.

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 a line tangent to the circle. Outward from the center of the circle along the direction at an angle of 45o with the radius of the circle. Along the radial direction away from the center of the circle. Along the radial direction toward the center of the circle.

Along the radial direction toward the center of the circle.

A free-body diagram consists of a closed outline of the external boundary of the system: Excluding all bodies which contact and exert forces on the system and replacing them by vectors representing the forces and moments they exert on the isolated system. Excluding all bodies which contact and exert forces on the system. Including all bodies which contact and exert forces on the system. Which does not contain any forces.

Excluding all bodies which contact and exert forces on the system and replacing them by vectors representing the forces and moments they exert on the isolated system.

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. Determine the mass of a body in terms of the distance of the body from a particular axis. Calculate the momentum of a body with respect to two different axes that are parallel. Express the moment of a force about one axis in terms of the moment of that force about a parallel axis.

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

According to Newton's Second Law: F = v / m, where F is the force, m is the mass, and v is the velocity. F = m / a, where F is the force, m is the mass, and a is the acceleration. F = m a, where F is the force, m is the mass, and a is the acceleration. F = m v, where F is the force, m is the mass, and v is the velocity.

F = m a, where F is the force, m is the mass, and a is the acceleration.

The instantaneous center of zero velocity must lie on the rotating body. True False

False

Select the one true statement from the four choices offered below: If the net resultant force acting on a particle is zero, then the angular momentum is conserved. If angular momentum is conserved, then linear momentum is also conserved. If linear momentum is conserved, then angular momentum is also conserved. If the resultant moment about a fixed point is zero, then the angular momentum about that point is conserved.

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. Kinetic energy. Power Potential energy.

Impulse and momentum.

According to Newton's Law of Gravitation the force of gravitational attraction between two particles is: Inversely proportional to the square of the distance between the centers of the particles. Inversely proportional to the distance between the centers of the particles. Directly proportional to the distance between the centers of the particles. Directly proportional to the square of the distance between the centers of the particles.

Inversely proportional to the square of the distance between the centers of the particles.

Angular momentum: Is calculated as the moment of linear momentum. Has the same direction as linear momentum. Is calculated as the moment of the net force about a particular point. Has the same direction as the net moment acting on the system.

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: Potential energy of the particles making up the mass system. Kinetic energy due to motion of all particles relative to the mass-center. Work done on the mass-system by the external forces. Kinetic energy of the mass-center translation.

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: Kinetic energy is conserved, but linear momentum is not conserved. Linear momentum is conserved, but kinetic energy is not conserved. Linear momentum and kinetic energy are both conserved. Neither linear momentum nor kinetic energy is conserved.

Linear momentum and kinetic energy are both conserved.

The product of mass with velocity is the: Kinetic Energy. Angular momentum. Linear momentum. Impulse.

Linear momentum.

The coefficient of restitution for an impact between two particles is the ratio of the: Magnitude of the restoration force to the magnitude of the deformation force. Incoming kinetic energy of the particles to the outgoing kinetic energy of the particles. Incoming momentum of the particles to the outgoing momentum of the particles. Magnitude of the restoration impulse to the magnitude of the deformation impulse.

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

Newton's second law relates force to: Weight and acceleration. Weight. Mass and acceleration. Mass and velocity.

Mass and acceleration.

The four fundamental quantities of mechanics are: Weight, length time, force. Mass, length, velocity, acceleration. Mass, length, acceleration, force. Mass, length, time, force.

Mass, length, time, force.

For steady mass flow conditions the flow may be described as ρ1v1A1=ρ2v2A2 for density, ρ, velocity, v, and area, A. This expression is a consequence of the conservation of: Energy. Angular momentum. Mass. Momentum.

Mass.

For particles moving along a plane curvilinear path, analysis of motion: Must use polar coordinates. May use normal and tangential coordinates or polar coordinates, but must not use rectangular coordinates. May use normal and tangential coordinates, polar coordinates, or rectangular coordinates. Must use normal and tangential coordinates.

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

The statement that the acceleration of a particle is proportional to the resultant force acting on it and is in the direction of this force is: Newton's First Law. Newton's Second Law. Newton's Third Law. Galileo's Law.

Newton's Second Law.

In the analysis of the motion of a rocket: Potential energy is conserved. Newton's third law does not apply. Newton's second law cannot be used in the form ∑F = ma because the mass of the rocket is not constant as a result of mass exhausted from the rocket. Newton's second law does not apply.

Newton's second law cannot be used in the form ∑F = ma because the mass of the rocket is not constant as a result of mass exhausted from the rocket.

For a rigid body: No net work is done by the internal interacting forces. The net work done by the internal interacting forces is equal to the change in kinetic energy of the rigid body. The net work done by the internal interacting forces is accompanied by an equal reduction in the gravitational potential energy of the rigid body. The net work done by the internal interacting forces is always negative.

No net work is done by the internal interacting forces.

A defined mass of liquid or gaseous particles flowing at a specified rate is an example of a: Semi-rigid body. Rigid body. Nonrigid body.

Nonrigid body.

When acted upon by a force of one pound a one slug mass will experience an acceleration of : 32.2 feet per second squared. One meter per second squared. One foot per second squared. 9.81 meters per second squared.

One foot per second squared.

The velocity vA/B represents the velocity of: Point A. Point A with respect to point B. Point B with respect to point A. Point A plus the velocity of point B.

Point A with respect to point B.

The time rate of doing work is the: Efficiency. Potential energy. Power. Kinetic energy.

Power

The magnitude of the velocity vector is called the: Speed and it is a scalar. Acceleration and it is a scalar. Speed and it is a vector. Acceleration and it is a vector.

Speed and it is a scalar.

The magnitude of the velocity is the: Displacement. Acceleration. Speed. Position.

Speed.

Consideration of rectilinear motion of an object can be simplified by treating the motion of the body as that of a particle if: The mass of the body is negligible. The forces acting on the body are non-concurrent. The analysis is concerned only with the motion of the center of mass. The dimensions of the object are small compared to those of surrounding objects.

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

The inertia of a particle is: Inversely proportional to the particle's mass. Calculated as the product of the particle's mass and its acceleration. The same as the particle's weight. The particle's resistance to rate of change of velocity.

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

Linear momentum is conserved if: There is external impulse acting on the mass system. Angular momentum of the mass system is zero. The net moment of all the external forces acting on the system is zero. The resultant external force acting on the mass system is zero.

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

A necessary condition for conservation of angular momentum of a particle is: The distance between the particle and the point about which the angular momentum is calculated must be zero. The resultant moment about a fixed point of all the forces acting on the particle must be zero. The linear momentum of the particle must be zero. The kinetic energy of the particle must be zero.

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

For steady mass flow conditions the time rate of change of the linear momentum is equal to: The vector sum of the external forces acting on the system. The total kinetic energy of the system. The time rate of change of the kinetic energy of the system. The time rate of change of the angular momentum of the system.

The vector sum of the external forces acting on the system.

A necessary condition for the conservation of angular momentum for a general mass system is that: Linear momentum is conserved. There is no angular impulse about a fixed point (or about the mass center). There is no net force acting on the system. Kinetic energy is conserved.

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

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: Momentum of the system. Work done on the system. Change in kinetic energy of the system. Time rate of change of the momentum of the system, assuming mass is constant in the system.

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

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 False

True

The number of coordinates required to specify the positions of all parts of a system having two degrees of freedom is: Two. One. Three. Four.

Two

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 = kx Ve=(1/2)kx Ve=(1/2)kx^2 Ve=-kx

Ve=(1/2)kx^2

The time derivative of a vector is a: Either a scalar or a vector. Tensor. Scalar. Vector.

Vector.

The slope of the displacement versus time curve is the: Velocity. Acceleration. Work done. Inverse of the velocity.

Velocity.

The relationship between weight W and mass m is W = mg. W = m. W = m/g. W = (1/2) mg2.

W = mg.

A rigid body is an object: That is always at rest. Whose dimensions are negligible. Whose changes in shape are negligible compared with the overall dimensions of the body or with the changes in position of the body as a whole. For which the dimensions are irrelevant to the description of its motion or the action of forces upon it.

Whose changes in shape are negligible compared with the overall dimensions of the body or with the changes in position of the body as a whole.

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/ρ)en+v˙ et a=(ρ v^2)en+v˙ et a=(v^2/ρ)en+v˙ et a=(v˙/ρ)en+v et

a=(v^2/ρ)en+v˙ et

For a rigid body in general plane motion the instantaneous center of zero velocity is a point that is always located on the object. about which the object may be considered to be in pure translation. about which the object may be considered to be in pure rotation. that is also the point of instantaneous center of zero acceleration.

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

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 = ω × (ω ×r). at = α × r. at = r × α. at = α × ω.

at = α × r.

For purely translational motion at all times every line in a body remains parallel to its original orientation. the object moves at a constant acceleration. at all times every line in a body moves in a direction perpendicular to its original orientation. the object moves at a constant velocity.

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 moves in a direction perpendicular to its original position. at all times every line in a body remains parallel to its original position. the object moves at a constant velocity. the object moves at a constant acceleration.

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

When a rigid body rotates about a fixed axis all points other than those on the axis move in concentric circles about the center of mass. on the body move in concentric circles. other than those on the axis move in straight lines. other than those on the axis move in concentric circles about the fixed axis.

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

The normal component of the relative acceleration due to rotation, (aA/B)n is r ω. r v. v/r. r ω^2.

r ω^2.

When using cylindrical coordinates for space curvilinear motion the coordinates used are: r, θ, z. r, x, y. x, y, z. r, θ, φ.

r, θ, z.

The kinetics of rigid bodies deals with translational motion only. the study of motion without reference to the forces which cause motion. rotational motion only. relating the action of forces on bodies to their resulting translational and rotational motions of the body.

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

The Coriolis acceleration always has a value of zero. is the same as the tangential acceleration. represents the difference between the acceleration of a point relative to another point on the object as measured from nonrotating axes and from rotating axes. is the same as the normal acceleration.

represents the difference between the acceleration of a point relative to another point on the object as measured from nonrotating axes and from rotating axes.

The equation ΣMG=H˙G states that the resultant moment about the mass center of the internal forces on the body equals the time rate of change of the linear momentum of the body. resultant moment about the mass center of the internal forces on the body equals the time rate of change of the angular momentum of the body about its center of mass. 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. resultant moment about the mass center of the external forces on the body equals the time rate of change of the linear momentum of the body.

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.

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: (m⁢v)⋅r. (m⁢v)×r. r×(m⁢v). r⋅(m⁢v).

r×(m⁢v).

The equation ΣF = m ā states that the sum of the internal forces acting on a body is equal to the weight of the body times the acceleration of the mass center of the body. sum of the internal forces acting on a body is equal to the mass of the body times the acceleration of the mass center of the body. sum of the external forces acting on a body is equal to the weight of the body times the acceleration of the mass center of the body. 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.

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 particles undergo translational motion only. all the particles are at rest. the distances between the particles remain unchanged. the particles undergo rotational motion only.

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

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 same angular acceleration and the same angular velocity, but they do not necessarily have the same angular displacement. the same angular displacement, but they do not necessarily have the same angular velocity. the same angular displacement and the same angular velocity, but they do not necessarily have the same angular acceleration.

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