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Class XIWeek 19: 7th September to 13th September, 2020 Name of Chapter: System of particles and Rotational motionDay 1, Day 2 & Day 3: Pg.No.154 to 162Step – IStudy the following topic from textbook:Chapter 7Section 7.7 to 7.8Step – IIStudy the same topic in the Extramark app:Step – IIIIf you have any doubts, clear them with your subject teacher. Step – IVRevise using the following bullet pointsTorque or moment of a force about the axis of rotation τ = r x F = rF sinθ n It is a vector quantity. If the nature of the force is to rotate the object clockwise, then torque is called negative and if rotate the object anticlockwise, then it is called positive. Its SI unit is ‘newton-metre’ and its dimension is [ML2T-2]. In rotational motion, torque, τ = Iα where a is angular acceleration and 1is moment of inertia.Moment of inertia: It is defined as the quantity expressed by the body resisting angular acceleration which is the sum of the product of the mass of every particle with its square of a distance from the axis of rotation. Or in more simple terms, it can be described as a quantity that decides the amount of torque needed for a specific angular acceleration in a rotational axis. Moment of Inertia?is also known as the angular mass or rotational inertia.?The SI unit of moment of inertia is kg m2. Moment of inertia is usually specified with respect to a chosen axis of rotation. It mainly depends on the distribution of mass around an axis of rotation. MOI varies depending on the axis that is chosen.Angular Momentum:The moment of linear momentum is called angular momentum. It is denoted by L. Angular momentum, L = I ω = mvr In vector form, L = I ω = r x mv Its unit is ‘joule-second’ and its dimensional formula is [ML2T-1]. Torque, τ = dL/dtConservation of Angular Momentum If the external torque acting on a system is zero, then its angular momentum remains conserved. If τext =?0, then L = I(ω) = constant ? I1ω1== I2ω2PRINCIPLE OF MOMENTS : If algebraic?sum of moments of all the forces acting on the body about the axis of rotation is zero, the body is in equilibrium.? According to the principle of moments, in equilibrium: Sum of anticlockwise Moments = Sum of clockwise momentsStep – VSolve the following questions in your C/W copy:Derive an expression for torque in a) Cartesian coordinates, b) polar coordinates.Express torque in rectangular components.Derive an expression for angular momentum in a) Cartesian coordinates, b) polar coordinates.Explain the geometrical meaning of angular momentum.State the principle of moments.End of Day 1,Day 2 & Day 3 Day 4, Day 5 (Numericals)Step – IFind the torque of a force?7i+3j??5k??about the origin. The force acts on a particle whose position vector is?i?j+k.A metal bar?70?cm?long and?4.00?kg?in mass supported on two knife-edges placed?10?cm?from each end. A?6.00?kg?load is suspended at?30?cm?from one end. Find the reactions at the knife-edges. (Assume the bar to be of uniform cross section and homogeneous.)A particle of mass?m?is released from rest from point?P?at?x=x0??on X-axis from origin?O, and falls vertically along y-axis as shown in Fig.What is the magnitude of the torque acting on the particle at time?t, when it is at the point?Q?w.r.t.?O?Find the angular momentum of the particle about O at time t. End of Week 19 ................
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