Force

• Force


  A push or pull that can cause an object to change its velocity, shape, or direction
• Translational motion


  • When a force acts on a rigid body which is free to move in a straight path in the direction of the force
• Translational motion


  • Linear motion of a ball
• Rotational motion


  • When a force is applied on a fixed point of a body which is pivoted at a point, then the body starts rotating about that point
• Rotational motion


  • Rotational motion of a wheel
• Moment (Turning effect) of a force or torque


  Force x Perpendicular distance of force from the axis of rotation
• Factors affecting the turning of a body are the magnitude of the force applied and the perpendicular distance of the line of action of the force from the axis of rotation
• Turning effect


  The moment of force (or torque) applied on the body about the body is due to
• Moment of force


  Force x distance
• Unit of moment of force


  • Nm or Newton x metre [SI]
  • CGS unit: 1 Nm = 10s dyne X 10² cm = 10th dyne
• Clockwise and anticlockwise moments

  • If the effect on the body is to turn it clockwise, the moment is taken positive
  • If the effect on the body is to turn it anticlockwise, the moment is taken negative
• Common examples of moment of force


  • To open or shut a door
  • For turning a steering wheel
  • In a Bicycle
• Couple


  When two equal and opposite parallel forces, not acting along the same line, form a couple
• Moment of Couple


  Either force x perpendical distance between the two forces (Couple arm)
• Equilibrium of Bodies


  When the resultant of all the forces acting on a body produce no change in its state of linear or rotational motion, the body is said to be in a state of equilibrium
• Types of equilibrium


  • Static equilibrium - when a body remains in a state of rest under the influence of several forces
  • Dynamic Equilibrium - when a body remains in the same state of motion under the influence of several forces
• Condition for equilibrium


  • The resultant of all the forces acting on the body should be zero
  • The algebraic sum of moments of all the forces acting on the body about the point of rotation should be zero
• Principle of Moments


  In equilibrium, Sum of clockwise moment = Sum of anticlockwise moment
• Verification of the principle of Moments

  1. Consider suspend some slotted weights w1 and w2 on the spring balance A and B respectively on either side of the thread

  2. Clockwise moment of weight w1 about the point O = w1 x L1

  3. Anticlockwise moment of weight w2 about the point O = w2 x L2

  4. Sum of anticlockwise moment = Sum of clockwise moment
• Position of centre of gravity

  • Rod - Mid point of rod
  • Circular disc - Geometric centre
  • Solid or hollow sphere - Geometric centre of the sphere
  • Solid or hollow cylinder - Mid point on the axis
  • Solid cone - At a height h/3 from the base, on its axis (h-height)
  • Hollow cone - At a height h/2 from the base, on its axis
  • Circular ring - Centre of ring
  • Triangular lamina - Point of intersection of the medians
  • Parallelogram/rectangular lamina - Point of intersection of the diagonals
• Difference between uniform linear motion and uniform circular motion

  • Uniform linear motion - Motion of body in straight line with constant velocity, no acceleration
  • Uniform circular motion - Motion of object in a circle with constant angular velocity, has radial acceleration towards the centre
• Centrifugal force acts from the centre, while centripetal force acts towards the centre during uniform circular motion
• Centrifugal force is not the force of reaction to centripetal force
• Centripetal and centrifugal forces are equal in magnitude