Distance is the. of a path followed by a particle. Distance is a quantity. The... of a particle is defined as its change in position in some time interval. Displacement is a.. quantity. The... of a particle is defined as the total distance traveled divided by the total time interval required to travel that distance: The average speed is the.. divided by the time interval. The average speed of a particle is a quantity. The. of a particle is equal to the ratio of the total distance it travels to the total time interval during which it travels that distance. The average velocity of a particle during some time interval is the... divided by the time interval. The definition of the average velocity is:. The average velocity of a particle is a quantity. The position of the particle is x(t)= 4 + t 2 + t 3, its average velocity between 1s and 3s is: The instantaneous velocity of a particle is defined as the.... The instantaneous velocity of a particle is the derivative of the versus... The instantaneous speed of a particle is equal to the of its instantaneous velocity. The velocity at any instant is the. of the tangent to the x -t graph at that instant. The of a particle is defined as the ratio of the change in its velocity divided by the time interval during which that change occurs. The definition of the average acceleration is:. The velocity of the particle is v(t)= 4 + t 2 + t 3, its average acceleration between 1s and 3s is: The instantaneous acceleration equals the derivative of the with respect to time.
The instantaneous equals the time rate of change of the velocity. The acceleration at any instant is the... to the v -t graph at that instant. The is the difference between its final position vector and its initial position vector: The direction of the instantaneous velocity vector at any point in a particle s path is along a line.. at that point and in the direction of motion. The acceleration vector in uniform circular motion is always. to the path and always points toward the. of the circle. For uniform circular motion, the acceleration vector can only have a component. to the path. For uniform circular motion, the acceleration vector can only have a component, which is toward the of the circle. The tangential acceleration component causes the change in the.... of the particle. The radial acceleration component arises from the change of the velocity vector. The of the particle measured by an observer in one frame of reference is the same as that measured by any other observer moving with constant velocity relative to the first frame. The acceleration of the particle measured by an observer in one frame of reference is the same as that measured by any other observer moving with relative to the first frame. Any reference frame that moves with constant velocity relative to an inertial frame is itself. frame. When no force acts on an object, the acceleration of the object is.. If an object does not interact with other objects, it is possible to identify a reference frame in which the object has.. acceleration. In the absence of....., when viewed from an inertial reference frame, an object at rest remains at rest and an object in motion continues in motion with a constant velocity. In the absence of....., when viewed from an inertial reference frame, an object at rest remains at rest and an object in motion continues in motion with a constant speed in a straight line. The tendency of an object to resist any attempt to change its velocity is called..... is an inherent property of an object and is independent of the object s surroundings and of the method used to measure it.
Mass is a... quantity The acceleration of an object is directly proportional to the acting on it. The magnitude of the acceleration of an object is inversely proportional to its.. Gravitational mass and inertial mass have the.. The action force is.. in magnitude to the reaction force and. in direction. The action and reaction forces act on. objects. When we apply Newton s laws to an object, we are interested only in. forces that act on the object. The magnitude of the force of static friction between any two surfaces in contact can have the values: The direction of the kinetic friction force on an object is.. to the surface with which the object is in contact and.. to the actual motion. The maximum force of static friction fs,max between an object and a surface is. to the normal force acting on the object. The direction of the force of kinetic friction fk is. the direction of motion of the object relative to the surface. The force of kinetic friction is proportional to the magnitude of the l force. In the limiting case for a falling object, when the magnitude of the resistive force equals the object s weight, the object reaches its... A small sphere of mass m is hung by a cord from the ceiling of a boxcar that is accelerating to the right. A noninertial observer in the boxcar claims that forces act on the sphere in order to cause the observed deviation of the cord from the vertical: the force of gravity, the tension int he string and.. A small sphere of mass m is hung by a cord from the ceiling of a boxcar that is accelerating to the right. A noninertial observer in the boxcar claims that the forces acing on the sphere in order to cause the observed deviation of the cord from the vertical: the.. A small sphere of mass m is hung by a cord from the ceiling of a boxcar that is accelerating to the right. An inertial observer on the platform claims that.. forces act on the sphere in order to cause the observed deviation of the cord from the vertical. A small sphere of mass m is hung by a cord from the ceiling of a boxcar that is accelerating to the right. An inertial observer on the platform claims that the forces acing on the sphere in order to cause the observed deviation of the cord from the vertical: the. An object falling through air reaches terminal speed when the net force acting on it is...
The work W done on a system by an agent exerting a constant force on the system is: The work done by the centripetal force is.. The work done by the net force equals the change in. of the system. The work kinetic energy theorem states that the net work done on a particle by external forces equals the change in the.. of the particle. The time rate of energy transfer is called. If an agent applies a force F to an object moving with a velocity v, the power delivered by that agent is: The work done by the component Fx of the varying force as the particle moves from xi to xf is exactly equal to the.. under the Fx - x curve. The sum of kinetic and potential energies is the.. energy of the system. An system is one for which there are no energy transfers across the boundary. The work done by a.. force on a particle moving between any two points is independent of the path taken by the particle. The work done by a conservative force on a particle moving through any closed path is.. The change in the potential energy of a system is equal to: The definition of the potential energy function associated to a conservative force is: The gravitational potential energy function is:. The potential energy function of the spring force is: The x component of a conservative force acting on an object within a system equals the negative derivative of the.. of the system with respect to x. The force F equals the negative of the gradient of the energy function.
For the potential energy curve shown in the figure (a) Determine whether the force Fx is positive, negative, or zero at the five points indicated. (b)indicate points of stable equilibrium. (c) Indicate points of unstable equilibrium. A particle moves along a line where the potential energy of its system depends on its position r as graphed in the figure. In the limit as r increases without bound, U(r) approaches +1 J. (a) Identify each equilibrium position for this particle. Indicate whether each is a point of stable, unstable, or neutral equilibrium. (b) The particle will be bound if the total energy of the system is in what range? Now suppose that the system has energy +3 J. (c) Determine the range of positions where the particle can be found, (d) its maximum kinetic energy,
(e) the location where it has maximum kinetic energy, and (f) the binding energy of the system that is, the additional energy that it would have to be given in order for the particle to move out to infinity. Ch 9 The linear momentum of a particle of mass m moving with a velocity v is defined as:. The time rate of change of the linear momentum of a particle is equal to the. acting on the particle. The total momentum of an isolated system at all times equals its.. momentum. The impulse momentum theorem: the impulse of the force F acting on a particle equals the change in the of the particle. The impulse of the force F acting on a particle over the time interval t = tf - ti :. In the impulse approximation we assume that one of the forces exerted on a particle acts for a short time but is much greater than any other force present. In an elastic collision the total (as well as total momentum) of the system is the same before and after the collision. In an inelastic collision the total kinetic energy of the system is.. before and after the collision (even though the momentum of the system is conserved). In a inelastic collision the colliding objects stick together. The x coordinate of the center of mass of n particles is defined: The y coordinate of the center of mass of n particles is defined: The z coordinate of the center of mass of n particles is defined: The center of mass of any symmetric object lies on. The velocity of the center of mass of the system: The acceleration of the center of mass of the system: The total linear momentum of the system equals the total mass multiplied by the... The net external force on a system of particles equals.. Internal forces change the motion of the center of mass of the system. Ch 10, Ch 11
The.. position of a rigid object is defined as the angle between a reference line attached to the object and a reference line fixed in space. The angular displacement of a particle moving in a circular path or a rigid object rotating about a fixed axis is:. The definition of the angular speed is: The definition of the angular acceleration is:.. The tangential speed of a point on a rotating rigid object equals the perpendicular distance of that point from the axis of rotation multiplied by the.. The tangential component of the linear acceleration of a point on a rotating rigid object equals the point s distance from the axis of rotation multiplied by the... The definition of the moment of inertia is: The rotational kinetic energy is:.. The parallel-axis theorem states that the moment of inertia about any axis parallel to and a distance D away from an axis through the center of mass: The magnitude of the torque associated with a force F acting on an object is. The torque acting on the particle is proportional to its, and the proportionality constant is the.. The net work done by forces in rotating a symmetric rigid object about a fixed axis equals the change in the object s... The linear speed of the center of mass for pure rolling motion is given by: The magnitude of the linear acceleration of the center of mass for pure rolling motion is: The total kinetic energy of a rolling object is the sum of the energy about the center of mass and the translational kinetic energy of the center of mass. The definition of the angular momentum L of a particle relative to the origin O is:.. The torque acting on a particle is equal to the time rate of change of the particle s. A particle in uniform circular motion has a.. angular momentum about an axis through the center of its path. The net external torque acting on a system about some axis passing through an origin in an inertial frame equals the time rate of change of the. momentum of the system about that origin.
The resultant torque acting on a system about an axis through the equals the time rate of change of angular momentum of the system regardless of the motion of the center of mass. The z component of angular momentum of a rigid object rotating about a fixed z axis is: The net external torque acting on a rigid object rotating about a fixed axis equals the moment of inertia about the rotation axis multiplied by the object s relative to that axis. If the net external torque acting on a system is zero, then the total angular momentum of the system is. Ch 12 A rigid object is in equilibrium if and only if the resultant force acting on it is zero and the resultant torque on it is zero about any axis: The elastic modulus is defined as the ratio of the. to the resulting. Young s modulus measures the resistance of a solid to a change in its... measures the resistance to motion of the planes within a solid parallel to each other Bulk modulus, which measures the resistance of solids or liquids to changes in their.. Ch 15 An object moves with simple harmonic motion whenever its. is proportional to its position and is... directed to the displacement from equilibrium. The.. T of the motion is the time interval required for the particle to go through one full cycle of its motion. The.. represents the number of oscillations that the particle undergoes per unit time interval. If a block spring system moves in simple harmonic motion the angular frequency is:. The angular frequency of a system moving in simple harmonic motion is determined by.. The amplitude and initial phase of a system moving in simple harmonic motion are determined by.. The potential energy of a particle performing simple harmonic motion is: The kinetic energy of a particle performing simple harmonic motion is: The total mechanical energy of a simple harmonic oscillator is a constant of the motion and is proportional to the square of the.
Close to the minimum any potential energy curve can be approached by a parabola, therefore for small displacements from the equilibrium position the system performs..... Uniform circular motion can be considered a combination of two simple harmonic motions, one along the x axis and one along the y axis, with the two differing in phase by... The period of a simple pendulum is:.. The period and frequency of a simple pendulum depend only on the and the. The period of a physical pendulum is:.. The frequency of the damped oscillator is... than the natural frequency. When the retarding force is small, the oscillatory character of the motion is preserved but the amplitude in time. If an oscillator experiences a damping force proportional to the velocity, its position for small damping is described by The forced oscillator vibrates at the frequency of the. The amplitude of the forced oscillator is a function of the.. of the driving force. When the frequency of the driving force is near the natural frequency of oscillation, the amplitude is. If the damping is less, the amplitude of oscillation at the resonance frequency is. At resonance the applied force is in...... with the velocity and the power transferred to the oscillator is a maximum. If an oscillator is subject to a sinusoidal driving force F(t) = F0 sin t, it exhibits resonance, in which the amplitude is largest when the driving frequency matches the. of the oscillator.