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MOTIO
  N
INTRODUCTION
• Mechanics, branch of physics concerning the motions
  of objects and their response to forces. Modern
  descriptions of such behavior begin with a careful
  definition of such quantities as displacement (distance
  moved), time, velocity, acceleration, mass, and force.
  Until about 400 years ago, however, motion was
  explained from a very different point of view. For
  example, following the ideas of Greek philosopher and
  scientist Aristotle, scientists reasoned that a cannonball
  falls down because its natural position is in the earth;
  the sun, the moon, and the stars travel in circles
  around the earth because it is the nature of heavenly
  objects to travel in perfect circles.
• The Italian physicist and astronomer Galileo brought
  together the ideas of other great thinkers of his time
  and began to analyze motion in terms of distance
  traveled from some starting position and the time that
  it took. He showed that the speed of falling objects
  increases steadily during the time of their fall. This
  acceleration is the same for heavy objects as for light
  ones, provided air friction (air resistance) is discounted.
  The English mathematician and physicist Sir Isaac
  Newton improved this analysis by defining force and
  mass and relating these to acceleration. For objects
  traveling at speeds close to the speed of
  light, Newton’s laws were superseded by Albert
  Einstein’s theory of relativity. For atomic and subatomic
  particles, Newton’s laws were superseded by quantum
  theory. For everyday phenomena, however, Newton’s
  three laws of motion remain the cornerstone of
  dynamics, which is the study of what causes motion.
NEWTON’S 3 LAWS OF MOTION
1. Newton’s first law of motion states that if the vector
   sum of the forces acting on an object is zero, then the
   object will remain at rest or remain moving at constant
   velocity. If the force exerted on an object is zero, the
   object does not necessarily have zero velocity. Without
   any forces acting on it, including friction, an object in
   motion will continue to travel at constant velocity.
2. Newton’s second law relates net force and
   acceleration. A net force on an object will accelerate
   it—that is, change its velocity. The acceleration will be
   proportional to the magnitude of the force and in the
   same direction as the force. The proportionality
   constant is the mass, m, of the object. F = ma
3. Newton’s third law of motion states that an object experiences
   a force because it is interacting with some other object. The
   force that object 1 exerts on object 2 must be of the same
   magnitude but in the opposite direction as the force that
   object 2 exerts on object 1. If, for example, a large adult gently
   shoves away a child on a skating rink, in addition to the force
   the adult imparts on the child, the child imparts an equal but
   oppositely directed force on the adult. Because the mass of the
   adult is larger, however, the acceleration of the adult will be
   smaller.
FRICTION
• Friction acts like a force applied in the direction opposite to an object’s
  velocity. For dry sliding friction, where no lubrication is present, the
  friction force is almost independent of velocity. Also, the friction force
  does not depend on the apparent area of contact between an object and
  the surface upon which it slides. The actual contact area—that is, the
  area where the microscopic bumps on the object and sliding surface are
  actually touching each other—is relatively small. As the object moves
  across the sliding surface, the tiny bumps on the object and sliding
  surface collide, and force is required to move the bumps past each other.
  The actual contact area depends on the perpendicular force between the
  object and sliding surface. Frequently this force is just the weight of the
  sliding object. If the object is pushed at an angle to the
  horizontal, however, the downward vertical component of the force
  will, in effect, add to the weight of the object. The friction force is
  proportional to the total perpendicular force.
M O T I O N (  P H Y S I C S    I  T E R M )
Let us draw AD parallel to OC. From the graph, we observe
                                that
                    BC = BD + DC = BD + OA
               Substituting BC = v and OA = u,
                       we get v = BD + u
                       or BD = v . u (8.8)
From the velocity-time graph (Fig. 8.8), the acceleration of the
                        object is given by
      a = Change in velocity/time taken = BD/AD = BD/OC
                  Substituting OC = t, we get
                            a = BD/t
                        Or BD = at (8.9)
               Using Esq. (8.8) and (8.9) we get
                           v = u + at
S = area OABC (which is a trapezium)
     = area of the rectangle OADC + area of the
                   triangle ABD
          = OA.OC + ½ (AD.BD) (8.10)
Substituting OA = u, OC = AD = t and BD= at, we
                         get
               s = u × t + ½(t ×at)
                s = u t + ½ (a t 2)
s = area of the trapezium OABC
               = OA + BC × OC × ½
 Substituting OA = u, BC = v and OC = t, we get
              S = (u+v)t × ½ (8.11)
From the velocity-time relation (Eq. 8.6), we get
                t = v – u/a (8.12)
     Using Eqs. (8.11) and (8.12) we have
                S = v + u v – u/2a
                  2 a s = v2 - u2
• WHEN AN OBJECT
  MOVES IN A
  CIRCULAR PATH WITH
  UNIFORM SPEED, ITS
  MOTION IS CALLED
  UNIFORM CIRCULAR
  MOTION.
• V = 2×22×r/7×t

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M O T I O N ( P H Y S I C S I T E R M )

  • 2. INTRODUCTION • Mechanics, branch of physics concerning the motions of objects and their response to forces. Modern descriptions of such behavior begin with a careful definition of such quantities as displacement (distance moved), time, velocity, acceleration, mass, and force. Until about 400 years ago, however, motion was explained from a very different point of view. For example, following the ideas of Greek philosopher and scientist Aristotle, scientists reasoned that a cannonball falls down because its natural position is in the earth; the sun, the moon, and the stars travel in circles around the earth because it is the nature of heavenly objects to travel in perfect circles.
  • 3. • The Italian physicist and astronomer Galileo brought together the ideas of other great thinkers of his time and began to analyze motion in terms of distance traveled from some starting position and the time that it took. He showed that the speed of falling objects increases steadily during the time of their fall. This acceleration is the same for heavy objects as for light ones, provided air friction (air resistance) is discounted. The English mathematician and physicist Sir Isaac Newton improved this analysis by defining force and mass and relating these to acceleration. For objects traveling at speeds close to the speed of light, Newton’s laws were superseded by Albert Einstein’s theory of relativity. For atomic and subatomic particles, Newton’s laws were superseded by quantum theory. For everyday phenomena, however, Newton’s three laws of motion remain the cornerstone of dynamics, which is the study of what causes motion.
  • 4. NEWTON’S 3 LAWS OF MOTION 1. Newton’s first law of motion states that if the vector sum of the forces acting on an object is zero, then the object will remain at rest or remain moving at constant velocity. If the force exerted on an object is zero, the object does not necessarily have zero velocity. Without any forces acting on it, including friction, an object in motion will continue to travel at constant velocity. 2. Newton’s second law relates net force and acceleration. A net force on an object will accelerate it—that is, change its velocity. The acceleration will be proportional to the magnitude of the force and in the same direction as the force. The proportionality constant is the mass, m, of the object. F = ma
  • 5. 3. Newton’s third law of motion states that an object experiences a force because it is interacting with some other object. The force that object 1 exerts on object 2 must be of the same magnitude but in the opposite direction as the force that object 2 exerts on object 1. If, for example, a large adult gently shoves away a child on a skating rink, in addition to the force the adult imparts on the child, the child imparts an equal but oppositely directed force on the adult. Because the mass of the adult is larger, however, the acceleration of the adult will be smaller.
  • 6. FRICTION • Friction acts like a force applied in the direction opposite to an object’s velocity. For dry sliding friction, where no lubrication is present, the friction force is almost independent of velocity. Also, the friction force does not depend on the apparent area of contact between an object and the surface upon which it slides. The actual contact area—that is, the area where the microscopic bumps on the object and sliding surface are actually touching each other—is relatively small. As the object moves across the sliding surface, the tiny bumps on the object and sliding surface collide, and force is required to move the bumps past each other. The actual contact area depends on the perpendicular force between the object and sliding surface. Frequently this force is just the weight of the sliding object. If the object is pushed at an angle to the horizontal, however, the downward vertical component of the force will, in effect, add to the weight of the object. The friction force is proportional to the total perpendicular force.
  • 8. Let us draw AD parallel to OC. From the graph, we observe that BC = BD + DC = BD + OA Substituting BC = v and OA = u, we get v = BD + u or BD = v . u (8.8) From the velocity-time graph (Fig. 8.8), the acceleration of the object is given by a = Change in velocity/time taken = BD/AD = BD/OC Substituting OC = t, we get a = BD/t Or BD = at (8.9) Using Esq. (8.8) and (8.9) we get v = u + at
  • 9. S = area OABC (which is a trapezium) = area of the rectangle OADC + area of the triangle ABD = OA.OC + ½ (AD.BD) (8.10) Substituting OA = u, OC = AD = t and BD= at, we get s = u × t + ½(t ×at) s = u t + ½ (a t 2)
  • 10. s = area of the trapezium OABC = OA + BC × OC × ½ Substituting OA = u, BC = v and OC = t, we get S = (u+v)t × ½ (8.11) From the velocity-time relation (Eq. 8.6), we get t = v – u/a (8.12) Using Eqs. (8.11) and (8.12) we have S = v + u v – u/2a 2 a s = v2 - u2
  • 11. • WHEN AN OBJECT MOVES IN A CIRCULAR PATH WITH UNIFORM SPEED, ITS MOTION IS CALLED UNIFORM CIRCULAR MOTION. • V = 2×22×r/7×t