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Assertion: Torque on a body may be non-zero even if the net force acting on it is zero.
Reason: Force does not depend on point of application, but torque depends on point of application.

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Important Questions on Rotational Mechanics

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A child’s top is spun with angular acceleration α=4t3-3t2+2t where t is in seconds and a is in radians per second-square. At t=0, the top has angular velocity ω0=2 rad s-1 and a reference line on it is at an angular position θ0=1 rad.
Statement I: Expression for angular velocity ω=2+t2-t3+t4 rad s-1

Statement II: Expression for angular position θ=1+2t-3t2+4t3 rad

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On account of the rotation of the earth about its axis,
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A fly wheel originally at rest is to attain an angular velocity of 36 rad s-1 in 6 s. The total angle it turns through which it turns in the 6 s is:-
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A rotating rod starts from rest and acquires rotational speed 600 revolutions/minute in 2 seconds with constant angular acceleration. The angular acceleration of the rod is
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Point masses of 1, 2, 3 and 10 kg are lying at the points (0, 0), (2 m, 0) (0, 3 m) and ( 2 m,  2 m) respectively in x-y plane. Find the moment of inertia of this system about  y-axis. (in kg m2).
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The moment of inertia of a ring and a disc of the same mass about their diameters are the same. What will be the ratio of their radii?
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Two rings have their moments of inertia in the ratio 4:1 and their diameters are in the ratio 4:1. Find the ratio of their masses.
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Two bodies of masses 1 kg and 2 kg are attached to the ends of a 2 m long weightless rod. This system is rotating about an axis passing through the middle point of the rod and perpendicular to the length. Calculate the M.I. of the system.