Assignment Made by: Shiva Athwal M-027/18 MPED-Ivth semester Linear Movement Responses To Applied Forces And Rotatory Movement Responses To Applied Torques UNIT 3 The word linear is used because straightening out the arc travelled by the object along the circle results in a line of same length. It is measured in Distance per unit Time. A Ɵ r B Formula for linear speed is as follows:- Speed= Distance Time S.I. unit is metre per seconds (m/s) • It simply refers to how quickly an object is rotating. • It is defined as change in angle of the object per unit time. A Ɵ r B Formula for angular speed is as follows:- Speed= Radian Time where, Radian is measuring angles and right angle is defined as P/2 radian It is denoted by Omega (ω) S.I. unit is Radian per Second. It is the rate of change of object’s position with respect to time. For example, speed of the runner when he/she is running. Formula for linear velocity is as follows:- V= d t Where, d= displacement (shortest distance covered between initial and final position) t= time taken to travel S.I. unit is metre per seconds (m/s) The rate of change in velocity at which an object is rotating around a centre or a specific point in a given time period. Formula for angular velocity is as follows:- Angular Velocity= Angular Displacement Time S.I. unit is Radian per Second. Linear acceleration is defined as rate of change of velocity. Ex- Running with a javelin. Formula for linear acceleration is as follows:- Linear acceleration= v-u/t Where, v= Final Velocity u= Initial Velocity t= Time S.I. unit of linear acceleration is km/h2 or m/sec2 Angular acceleration is defined as rate of change of angular velocity. Example, hammer throw Formula for angular acceleration is as follows:- Angular Acceleration= v-u t S.I. unit of angular acceleration is Revolution/Sec2 or Radius/ Sec2 Linear momentum is defined as the product of mass of an object and velocity of the object. Its a vector quantity, the direction of the momentum is the same as its velocity. Formula for linear momentum is as follows:- Linear momentum= m x v where, m= mass of the object v= velocity S.I. unit of linear momentum is kg m/s In an axis of rotation, the product of moment of inertia (I) and angular velocity (ω) is known as Angular Momentum. Formula for angular momentum is as follows:- H= I x ω S.I. unit of angular momentum is kg m2/sec When a FORCE acts on an object for a short amount of time, impulse is the measure of how much the force changes the momentum of an object. Formula for linear impulse is as follows:- Linear Impulse= Force x Time S.I. unit of linear impulse is kgm/s or Ns When you are applying force to a rotating system or a torque to that system it is called Angular Impulse. Example - punching a tether ball. Formula for Angular Impulse is as follows:- L= I x W where, L= Angular Impulse I= Rotating Inertia W= Angular Velocity S.I. unit of Angular Impulse is Nm/s Kinetic Energy is the energy possessed by the body due to its motion. Formula for kinetic energy is as follows:- K.E.= ½ mv 2 where, m= Mass of an object v= Final Velocity S.I. unit of Kinetic Energy is Joules (J). LINEAR MOVEMENT RESPENSES TO APPLIED FORCES & ROTATRY MOVEMENT RESPENSES TO APPLIED TORQUE CONTENT Relationship between Force , Mass & Acceleration Relationship of Centripetal force & Radial Acceleration . Relationship of Torque between Rotational Inernia & Angular Acceleration . This relation is based upon Newton’s Second Law of Motion, which states that force is developed in proportion of product of mass and acceleration of an object. F= m.a F∞a F∞m If we will increase or decrease, Acc., mass. it will affect force hence, force will also increase or decrease while keeping the mass constant. Relationship between Centripetal Force and Radial Acceleration C.F.= MV2 r Where, r = Radius M= Mass V= Velocity Based on Newton’s Second Law : F = m.a C.F = M.푽ퟐ r Radial Acceleration Acceleration towards the center along the radius is known as Radial Acceleration. If velocity is kept “constant” And radius is greater , C.F. will be less. And radius is less, C.F. will be more. C.F. ∞ 1 ( inversely proportionate) r Relationship between Torque, Rotational Inertia and Angular Acceleration Torque- A force that tend to cause rotation. It helps in turning effect. Eg. Opening a door Based on Newton’s Second Law F = m.a τ = Iα Where, I= Momentum of Inertia α= Angular Acceleration τ∞α τ∞α Directly proportinate τ∞I Directly proportinate .