Ans. Tangential velocity (v) “The linear velocity, along the direction of the tangent at any point on that curve which is followed by the moving particle”. Angular velocity (ω): “The rate of change of angular displacement of a particle moving along a curved path”. Difference: Both are related as : v = r ω The direction of ω is perpendicular to the plane of motion and the direction of
v is along tangent of the curved path. To find If one quantity is given with known radius, the other can be found from v = r ω
Q.2 Explain what is meant by centripetal force and why it must be furnished to an object if the object is to follow a circular path?
Ans. Centripetal force (Fc ): “The force needed to move a body around a circular path”. Mathematically, F = mv2 / r = mr ω2 Its direction is towards the center of the circle. Fc is furnished for an object moving in a circular path (of constant radius). For m & r constant, F ∝ ω2 , Its direction needs to be changed at every point, for it, a continuous perpendicular force is required.
Q.3 What is meant by moment of inertia? Explain the significance.
Ans. Moment of inertial (I): “Corresponding quantity for mass in rotatory motion”. Mathematically, I = Σ m r2 , where m is the mass of an element distant r from the axis. Significance: It’s a quantitative property of a solid which represent its resistance to rotation about a fixed axis. I plays the same role in angular motion as that of mass in linear motion.
Q.4 What is meant by angular momentum? Explain the law of conservation of angular
momentum.
Ans. Angular momentum: “The cross product of position vector and linear momentum”. Mathematically,
L = r x p. Also L = I ω Law of conservation of angular momentum: “If no external torque acts on a system, the total angular momentum of the system remains constant”. Mathematically, Ltotal = L1 + L2 + …..= constant or L = I1 ω1 = I2 ω2 = constant If I will increase, ω will increase and vice versa.
Q.5 Show that orbital angular momentum Lo = mvr.
Ans. We have L = I ω = (Σ mi ri2 ) ω For a body of mass, m L = I ω = m(Σ ri2 ) ω For orbital angular momentum having a constant orbit, r Lo = mr2 (v / r) [ω = v/r] or Lo = m v r
Q.6 Describe what should be the minimum velocity, for a satellite, to orbit close to the
Earth around it.
Ans. Fg = Gms M = me v2 = Fc or v = √GM / r r2 r or v = √gr2 / r = √ g r for minimum velocity of the satellite, g = 9.8 m/sec2 vmin = √ g r = √ 9.8x 6400 = 7.9 km/sec
Q.7 State the direction of the following vectors in simple situations; angular momentum
and angular velocity.
Ans. Direction of angular momentum (L) The expression for angular momentum is,
L = r x p Its direction is perpendicular to r & p, and is determined by right hand rule of cross product. Direction of angular velocity (ω) When a particle have circular motion in anti-clockwise direction, its direction of ω will be in upward direction (by applying right hand rule).
Q.8 Explain why an object, orbiting the Earth, is said to be freely falling. Use your explanation to point out why objects appear weightless under certain circumstances.
Ans. An object is given certain tangential velocity for orbiting the earth. It is like freely falling due to force of gravity. It will follow curved path due to two forces. The curvature of its path will match the curvature of the earth. Its centripetal acceleration equals its acceleration due to gravity; i.e. a = g, so T = mg – mg = 0. Hence it appears weightless.
Q.9 When mud flies off the tyre of a moving bicycle, in what direction does it fly?Explain.
Ans. The mud will fly in a direction tangent to the wheel. When mud separates from the tyre, centripetal force is ceased from the mud particles.
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Q.10 A disc and a hoop start moving down from the top of an inclined plane at the same time. Which one will be moving faster on reaching the bottom?
Ans. The disc will move faster down the bottom. PE = KEtran. + KErot. For disc: mgh = ½ mv2 + ½ Iω2 = ½ mv2 + ½ (1/2 mr2) v2 /r2 ⇒ v = √ 4gh / 3 for loop: mgh = ½ mv2 + ½ Iω2 = ½ mv2 + ½ (mr2) v2 /r2 ⇒ v = √ gh as √ 4gh / 3 > √ gh or vdisc > vhoop
Q.11 Why does a diver change his body positions before diving in the pool?
Ans. To increase angular velocity, the diver changes his body positions. L = I ω = mr2 ω For smaller r, ω will be greater. The diver closed his legs and arms to make smaller r so that his angular velocity increases to make more somersaults.
Q.12 A student holds two dumb-bells without stretched arms while sitting on a turntable.He is given a push until he is rotating at certain angular velocity. The student then
pulls the dumbbell towards his chest. What will be the effect on rate of rotation?
Ans. His rate of rotation will increase, due to smaller r, the distance from the axis of the distribution of mass m. L = I ω = mr2 ω When he pulls the dumbbells towards his chest, his moment of inertia decreases and he spins faster.
Q.13 Explain how much minimum number of geo-stationary satellites are required for global coverage of T.V. transmission.
Ans. Three correctly positioned satellites are sufficient for global coverage of TV transmission. As one such satellite covers 120 of longitude; (120o + 120o + 120o = 360o)
Question within the chapter bhe plz hamay dyn.. kindly.!
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