physics

-The force F depends only on the particle's position, not on the particle's velocity or time. -For any two points 1 and 2, the work done going from point 1 to point 2 by F is the same for all paths between points 1 and 2.

A force F on a particle is conservative if and only if that force satisfies two conditions. Select those two conditions from this list: -The sum of the total kinetic energy and the total potential energy will depend on the path and on time. -The potential energy will depend on both time and position, and have a minimum at a turning point. -The force F depends only on the particle's position, not on the particle's velocity or time. -For any two points 1 and 2, the work done going from point 1 to point 2 by F is the same for all paths between points 1 and 2.

thrust.

A rocket expels mass m with an exhaust velocity -vex. The product -mvex for a rocket is often called

will become under-damped.

A storm door/spring/damper system is initially tuned to be critically damped. If the door is modified such that the mass of the door increases (perhaps by attaching a heavy picture to it, or adding a heavy coat of weatherproofing paint), the door/spring/damper system

All the above are advantages of the Lagrangian formalism.

Advantages of using the Lagrangian formulation of dynamics include: All the above are advantages of the Lagrangian formalism. Uses scalar functions like the kinetic energy T and the potential energy U rather than vector functions like the momentum p. , Avoids the vector notation used in the Newtonian formulation. , The ability to take advantage of coordinates that exploit the symmetries and constraints of the physical circumstances of a problem.

any reference frame where Newton's First Law (also called "The Law of Inertia") holds.

An inertial reference frame is...

The plumb line points slightly southward of a line running from the suspension point to the center of the Earth.

Assume that the Earth is a uniform sphere rotating about its axis in its usual counter-clockwise direction (that is, west to east). A plumb line hangs motionless from a suspension point above a point on the surface of the Earth in the Northern Hemisphere some distance away from the North Pole. The plumb line hangs such that...

π/2 or 90 degrees

At resonance for a system with weak damping, the phase angle between the driving force and the response of the system is equal to

The magnitude of the total angular momentum of the system is constant. , The direction of the total angular momentum of the system is constant. , All motion occurs completely in a plane perpendicular to the total angular momentum vector.

For a central force problem written in terms of the center-of-mass frame, select all of the following which are correct statements: , The magnitude of the total angular momentum of the system is constant. , The direction of the total angular momentum of the system is constant. , The relative position vector is constant. , All motion occurs completely in a plane perpendicular to the total angular momentum vector.

the velocity of the particle in that particular dimension to decrease by a factor of 1/e.

For both quadratic and linear drag in one dimension, we defined a combination of variables called the characteristic time τ. The characteristic time is the time needed for

the equations of motion for the horizontal and vertical directions were coupled.

For projectile motion with quadratic drag, we could not get an analytical solution for the motion of the particle because

a holonomic constraint

If a constraint can be expressed as an equality involving the generalized coordinates (but not velocities) and/or time, the constraint is said to be

a scleronomic constraint.

If a constraint equation is not explicitly a function of time, the constraint is said to be

a constant of the motion

If a coordinate is an ignorable coordinate, the generalized momentum associated with that generalized coordinate is

a constant because the energy lost to damping is replaced by the driving force.

If a driven damped harmonic oscillator system is oscillating such its motion given by only the steady-state solution of the equations of motion, the total mechanical energy averaged over one period of oscillation is

-The force F may be written as the gradient of a potential energy function U: F(r)=−∇U(r). -The total work performed when a particle moves in a closed path under the influence of this force is zero. -The force F satisfies the relationship ∇×F(r)=0. -The work done on a particle by the force between any two points is independent of the path taken.

If a force F is conservative, which of the following will be true of F? (Note that there may be more than one answer you'll need to mark.) -The force F may be written as the gradient of a potential energy function U: F(r)=−∇U(r). -The total work performed when a particle moves in a closed path under the influence of this force is zero. -The force F satisfies the relationship ∇×F(r)=0. -The work done on a particle by the force between any two points is independent of the path taken.

the square of the particle's velocity.

If a particle experiences Newtonian drag, the resistive force is directly proportional to

2 * pi * squareroot (m/k)

If a particle has mass m and is connected to a spring with spring constant k, the period of oscillation will be

mx¨+bx˙+kx=0

If a particle of mass m that is connected to a spring with spring constant k and is subjected to a velocity-dependent damping force given by −bx˙, the equation of motion for the system is

will lie on that axis

If a system of particles or a solid body is rotationally symmetric about some axis, the center of mass will

the total mechanical energy, defined as the sum of the particle's kinetic and potential energies, is constant in time.

If all the forces Fi acting on a particle are conservative, each with its corresponding potential energyUi, then

is given by the net external torque on the system.

If all the internal forces acting within a system of N particles are central forces, then we know that the time derivative of the total angular momentum

an ignorable coordinate

If the Lagrangian does not explicitly depend on a particular coordinate (say, qk), then we say that the coordinate qk is

a hyperbola

If the eccentricity for the orbit of a particle in a central inverse-square field is greater than one, the orbit the particle follows is

False

If the equation of motion for a damped harmonic system is mx¨+bx˙+kx=0, the system will lose energy at a rate given by -bx˙^2

The center-of-mass coordinate R is an ignorable coordinate.

If the generalized coordinates used in the Lagrangian for the two-body central force problem are the relative separation of the two bodies and the center-of-mass coordinate R for the system, which of the following is true? The relative separation r is an ignorable coordinate. , Both the relative separation r and the center-of-mass coordinate R are ignorable coordinates. , The center-of-mass coordinate R is an ignorable coordinate. There are no ignorable coordinates in the problem.

is constant.

If the net external force F on a system of N particles is zero, the system's total mechanical momentum P

is constant.

If the net external torque Gnet acting on a system of N particles is zero, the total angular momentum L of the system

a torque must be supplied to maintain the relative orientation of the angular momentum L and the angular velocity ω. Answer, the total angular momentum L is not parallel to the angular velocity. Answer, the direction of the angular momentum L continuously changes.

If the products of inertia for an object are non-zero, Answer, a torque must be supplied to maintain the relative orientation of the angular momentum L and the angular velocity ω. Answer, the total angular momentum L is parallel to the angular velocity. Answer, no torque is required to get the object to spin stably about any axis. Answer, the direction of the angular momentum L stays constant. Answer, the total angular momentum L is not parallel to the angular velocity. Answer, the direction of the angular momentum L continuously changes.

a hyperbola

If the total mechanical energy of a particle in an inverse-square field is greater than zero, the orbit of the particle will be:

f=N*k-c

If there are N particles in a system moving in k dimensions, and there are c equations of constraint available for the system, the total number of degrees of freedom f (and hence the number of generalized coordinates) is

U(x) is a minimum and d2U/dx2>0.

In a conservative one-dimensional system, a stable point of equilibrium occurs at the point r=a when

False

In a one-particle system, if a particular generalized coordinate is an ignorable coordinate, then that particular generalized coordinate is not needed in describing the position of the particle as a function of time. True False

a choice of spatial origin and axes to label positions in space and a choice of temporal origin to measure times.

In classical mechanics, a reference frame is

found from Newton's Second Law

In classical mechanics, the differential equations called the "equations of motion" generally are

a symmetric top

In terms of its principal axes, a Frisbee (spinning disk) is considered

Coriolis force

In the general formula for the force in a non-inertial reference frame: F→=F0→−mA→−mΩ→˙×r→−2mΩ→×v→−mΩ→×Ω→×r→ the term −2mΩ→×v→ is called the:

centrifugal force

In the general formula for the force in a non-inertial reference frame: F→=F0→−mA→−mΩ→˙×r→−2mΩ→×v→−mΩ→×Ω→×r→ the term −mΩ→×Ω→×r→ is called the:

transverse force

In the general formula for the force in a non-inertial reference frame: F→=F0→−mA→−mΩ→˙×r→−2mΩ→×v→−mΩ→×Ω→×r→ the term −mΩ→˙×r→ is called the:

x(t)=Acos⁡(ωt−δ) x(t)=B1e(−iωt)+B2e(iωt) x(t)=C1cos(ωt)+C2sin(ωt)

Indicate which of the following equations represent solutions of the simple harmonic oscillator equation of motion mx¨+kx=0: x(t)=Acos⁡(ωt−δ) x(t)=Ae(Bt)cos(ωt−δ) x(t)=B1e(−iωt)+B2e(iωt) x(t)=C1cos(ωt)+C2sin(ωt)

conic sections.

Kepler's laws indicate that all objects moving in an inverse-square attractive force field will move in orbits that are

The square of the orbital period for a planet is proportional to the cube of the semi-major axis for that planet's orbit.

Kepler's third law of motion states that

False

Lagrangian dynamics can only be used for systems where the forces acting are conservative. True False

E=U(a)

Suppose for a conservative force, the total mechanical energy is E, the kinetic energy is T(r), and the potential energy is U(r). In a potential energy diagram, a "turning point" occurs at r=a if

In the absence of forces, a particle will move with constant velocity.

One way to correctly state the "Law of Inertia" is

The velocity of the center of mass for the two-particle system is constant. , The central force conserves the total mechanical energy - kinetic plus potential - for the two particles. , The central force is a function of the distance between the two particles and acts along a line between the two particles. , The total angular momentum of the two-particle system is constant

Select all true statements for an isolated system of two particles with a central force acting between them: , The velocity of the center of mass for the two-particle system is constant. , The central force conserves the total mechanical energy - kinetic plus potential - for the two particles. , The central force is a function of the distance between the two particles and acts along a line between the two particles. , The total angular momentum of the two-particle system is constant

-A period of oscillation that is independent of the amplitude of the motion. -Oscillations in displacement that are periodic in time. -Oscillations that are symmetric about the point of equilibrium.

Simple harmonic motion is characterized by which of the following (check all that apply) -A period of oscillation that is independent of the amplitude of the motion. -Oscillations in displacement that are periodic in time. -Oscillations that are symmetric about the point of equilibrium. -A period of oscillation that depends on the amplitude of the motion.

In the absence of forces, a particle moves with constant velocity v.

Sometimes called the "law of inertia", Newton's First Law states

False

True or False: The electrostatic force between two charges (which is called the Coulomb force) is not a conservative force.

Arise in non-inertial reference frames because of the translational and/or rotational motion of the non-inertial reference frame.

The "fictitious forces" (also called "pseudo-forces") found in a non-inertial reference frame...

True

The Earth is an example of a non-inertial reference frame. True False.

The Earth rotates on its axis relative to an inertial reference frame defined by the stars.

The Foucault pendulum is important because it demonstrates that...

L=T-U

The Lagrangian L for conservative systems is defined as

a charged particle moving in electric and magnetic fields.

The Lorentz force is the force experienced by

False

The Lorentz force, the force acting on a charged particle moving through a magnetic field given by F=q(v×B), is an example of a central force. True False

the relative importance of quadratic drag versus linear drag.

The Reynolds number is an indication of

the frequency sqrt(ω0^2−2β^2).

The amplitude A(ω) for the motion of a driven damped harmonic oscillator will be greatest when the driving frequency is equal to

the work done by the net force on the particle between the two points.

The change in a particle's kinetic energy between two neighboring points on its path is equal to

True

The electrostatic (Coulomb) and gravitational forces (the "classical" forces) are central forces. True False

False

True or False: The two "classical" forces - the gravitational force and the electrostatic force - are not central forces.

what is the position of the particle r for all times t within that time interval?"

The fundamental goal of mechanics is "Given the total force acting on a particle during some time interval,

Ce(−βt)cos⁡(ω1t−δtr).

The general solution to the equation of motion for the driven damped oscillator driven by a force F0cos⁡(ωt) is given by the equation x(t)=Acos⁡(ωt−δ)+Ce−βtcos⁡(ω1t−δtr).The transient term of this general solution is

depends on both the shape of the object and its mass, as well as the viscosity of the medium.

The terminal speed of an object falling through a resistive medium

True

True or False: All central forces that are spherically symmetric are conservative.

True

True or False: For an N particle system, the center of mass R is the weighted average position for that system, where each particle's position ri is weighted by that particle's mass mi.

True

True or False: If a force F(r) between two objects is a central force, then that force acts along a line which joins the two objects.

True

True or False: If the potential energy function U is time dependent, the total mechanical energy is not constant in time.

True

True or False: Newton's Universal Law of Gravitation (i.e., the gravitational force) between two masses is a conservative force.

All central forces are conservative forces.

Which of the following statements is true? All central forces are non-conservative forces. , All conservative forces are central forces. , All central forces are conservative forces. Non-conservative forces are central forces.

true

each one of Euler's equations describes how the angular velocity changes as a function of time based on the components of the applied torque

false

eulers equations are an uncoupled set of differential equations that describe how the velocity changes as a function of time based on one component of the applied torque true or false

can be found by diagonalizing the moment of inertia tensor

for a general rigid body in cases where we cannot use symmetry to identify at least one principal axis all three principal axes

true

if a body has a symmetry axis that axis is a principal axis true or false

not asymmetric

in terms of its principal axes an American football is considered

Qk=-partialU/partialqk

the generalized force Qk for a conservative force is given by

stable about the axes with the largest and smallest moments of inertia, but unstable about the intermediate axis

the intermediate axis theorem states that if an object has three unequal principal moments of inertia, the rotation of the object will be

lambda1=lamba2=/lambda3

the three principal moments of inertia for a symmetric top obey the relationship

lambda1=/lambda2=/lambda3

the three principal moments of inertia for an asymmetric top obey the relationship