Physics

Session Rotational Mechanics - 3

Session Objectives

Session Objective 1.Torque Definition 2.Torque and Angular Acceleration Relationship 3.Kinetic Energy in Rotational Motion 4.Power Delivered in Rotational Motion 5.Work Done in Rotational Motion

F r O O d Moment arm Line of action F r r Torque Definition

X Y Om r Remember F=ma? What m is to force, I is to torque. Z What v is to P, is to L Remember P=mv? Where P is Linear momentum. Torque and Angular Acceleration Relationship

Since is constant I is Moment of Inertia P o riri ViVi m i y x Kinetic Energy in Rotational Motion

Power Delivered in Rotational Motion The rate of increase of kinetic energy equals the rate at which work is done on it, i.e. the power delivered by the torque

Work Done in Rotational Motion Work done in an infinitesimal angular displacement Thus, the work done during an angular displacement

Class Test

Class Exercise - 1 One end of a ladder is resting on a wall and the other end on the ground. Assume the weight of the ladder to be mg, the length of the ladder and the angle of inclination to the horizontal is . Find out the total torque about the lowermost point of the ladder.

Solution Taking moment about A mg  B N R A Where N and R are the reactions of the wall and the floor respectively.

Class Exercise - 2 Find out the total torque acting about point A in the diagram shown below.

Solution

Class Exercise - 3 Four equal and parallel forces are acting on a rod as shown in figure at distances 20 cm, 40 cm, 60 cm and 80 cm respectively from one end of the rod under the influence of these forces the rod (a) Is at rest (b) Experiences a torque (c) Experience a linear motion (d) Experience of torque and also linear motion

Solution As net force is zero it will not perform linear motion. Now taking torque about O, Hence, it experiences a torque. Therefore the answer is (b).

Class Exercise - 4 The moment of inertia of a wheel about the axis of rotation is 3.1 mks units. Its kinetic energy will be 600 J if the period of rotation is (a)0.05 s(b) s (c) 3.18 s(d) 20 s

Solution T = s Hence, answer is (b).

Class Exercise - 5 Four masses are fixed on a massless rod as shown in the following figure. The moment of inertia about the axis P is (a)2 kg m 2 (b) 1 kg m 2 (c) 0.5 kg m 2 (d) 0.3 kg m 2 2 kg 5 kg 0.2 m P

Solution I = 0.3 kg-m 2 Hence, answer is (b).

Class Exercise - 6 Two racing cars of masses m 1 and m 2 are moving in circles of radii r 1 and r 2 respectively. Their speeds are such that they make a complete circle in the same length of time t. The ratio of the angular speed of the first to the second car is (a)m 1 : m 2 (b) r 1 : r 2 (c) 1 : 1(d) m 1 r 1 = m 2 r 2

Solution Alternative solution Hence, answer is (c).

Class Exercise - 7 A meter stick is held vertically with one end on the floor and is allowed to fall. The speed of the other end when it hits the floor (assume that the other end at the floor does not slip). (a)3.2 m/s(b) 5.4 m/s (c) 7.6 m/s(d) 9.2 m/s

Solution Conservation of energy: v = 5.4 m/s Hence, answer is (b).

Class Exercise - 8 An inclined plane makes an angle of 30 o with the horizontal. A ring rolling down the inclined plane from rest without slipping has a linear acceleration equal to

Solution Hence, answer is (d).

Thank you