07%20%20-%20%20Rotational%20%20Motion

07%20%20-%20%20Rotational%20%20Motion - 7 ROTATIONAL MOTION...

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7 - ROTATIONAL MOTION Page 1 1 ) The minute’s hand of a watch is 2 cm long. Find ( a ) the angular velocity, ( b ) linear velocity and ( c ) the radial acceleration. [ April, 2002 ] [ Ans: ( a ) π / 1800 rad / s, ( b ) π / 900 cm / s, ( c ) ( π 2 / 162 ) × 10 4 cm / s 2 ] ( Note: Linear velocity and radial acceleration are for a particle on the tip of the minute’s hand of the watch. ) 2 ) The length of a simple pendulum is one metre and mass of its bob is 10 gram. If the angular displacement is 36 ° , find the angular acceleration. [ October, 1998 ] ( Ans: 5.76 rad / s 2 ) 3 ) A force ^ ^ ^ k j 2 i 2 + + = F is acting at a point = r ^ ^ ^ k j 2 i 2 + + away from the axis of rotation. Find the torque acting on it. [ March, 1998 ] ( Ans: zero ) 4 ) The position vector of a particle is = r ^ ^ ^ k j 2 i 2 + + and the force acting on is . F ^ ^ ^ k 7 j 6 i 5 + + = Calculate the torque acting on the particle. [ October, 1997 ] ( Ans: ^ ^ ^ k 2 j 9 i 8 - + ) 5 ) What should be the maximum speed of a vehicle when it passes on the inclined curved path ? The radius of the curved path is 200 metre and slope θ = 11 ° 32 . ( The path is frictionless ). [ March, 1997 ] ( Ans: 20 m / s ) ( Note: The problem is incorrectly framed. The path cannot be frictionless. The car cannot run on a frictionless path. At a very low speed, the car will have a tendency to slide inwards on the inclined path resulting in outward radial frictional force on its tyres. As the speed increases, this outward radial frictional force reduces and becomes zero at a definite speed. The answer given is this definite speed at which there is no radial frictional force on the tyres of the car and which the author intends to ask. If the speed of the car increases further, car will have a tendency to skid outwards and inward radial frictional force acts on its tyres which increases with speed of the car. At a certain maximum speed of the car, this frictional force reaches a maximum value. If the speed of the car exceeds this maximum value, it will skid outwards, assuming that the outward toppling speed is higher than this speed which is true for a vehicle
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This note was uploaded on 11/28/2011 for the course PHYSICS 300 taught by Professor Smith during the Spring '06 term at ITT Tech Flint.

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07%20%20-%20%20Rotational%20%20Motion - 7 ROTATIONAL MOTION...

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