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11th ICSE
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A hoop of radius r and mass m rotating with an angular velocity ω0 is placed on a rough horizontal surface. The initial velocity of the centre of the hoop is zero. What will be the velocity of the centre of the hoop when it ceases to slip?

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Important Questions on Rotational Motion of a Rigid Body : Moment of Inertia

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11th ICSE
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A thin horizontal circular disc is rotating about a vertical axis passing through its centre. An insect is at rest at a point near the rim of the disc. The insect now moves along a diameter of the disc to reach its other end. During the journey of the insect, the angular speed of the disc.
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11th ICSE
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A uniform rod of length (L) and mass (M) is pivoted at the centre. Its two ends are attached to two springs of equal spring constants (k) The springs are fixed to rigid supports as shown in the figure, and the rod is free to oscillate in the horizontal plane. The rod is free to oscillate in the horizontal plane. The rod is gently pushed through a small angle (theta) in one direction and released. The frequency of oscillation is. ?

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EASY
11th ICSE
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If the resultant of all the external forces acting on a system of particles is zero, then from an inertial frame, one can surely say that:

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11th ICSE
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A thin uniform rod, pivoted at O, is rotating in the horizontal plane with constant angular speed ω, as shown in the figure. At time t=0 a small insect starts from O and moves with constant speed v with respect to the rod towards the other end. It reaches the end of the rod att=T and stops. The angular speed of the system remains ω throughout. The magnitude of the torque ∣τ∣ on the system about O, as a function of time is best represented by which plot?

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11th ICSE
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A ball  is confined to move in  a circular path decreasing linear speed, Choose the correct statement
MEDIUM
11th ICSE
IMPORTANT

The moment of inertia of thin square plate ABCD of uniform thickness about an axis passing through the center O and perpendicular to the plane of the plate is. 

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11th ICSE
IMPORTANT

For the given uniform square lamina ABCD, whose centre is O,

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MEDIUM
11th ICSE
IMPORTANT

Consider a uniform square plate of side a and mass m. The moment of inertia of this plate about an axis perpendicular to its plane and passing through one of its corner is