Rotational Motion Questions
-- 3. The instantaneous angular position of a point on a rotating wheel is given by the equation θ(t) = 2t³ - 6t². The torque on the wheel becomes zero at
-- 2. Which of the following has the highest moment of inertia when each of them has the same mass and the same radius?
1. Moment of inertia of a rigid body depends on
A uniform solid sphere (mass M, radius R) rolls without slipping on a flat surface. The fraction of its total KE that is rotational is:
The relationship between angular velocity ω, linear velocity v, and radius r is:
A thin ring and a solid disc of same mass and radius start rolling from rest down an inclined plane. Ratio of their velocities at the bottom is:
The radius of gyration of a solid sphere of radius R about its diameter is:
A horizontal platform rotates freely. A man standing at the edge walks towards the centre. The angular speed of the platform will:
Two bodies with moments of inertia I₁ and I₂ (I₁ > I₂) have equal angular momenta. The ratio of their kinetic energies E₁/E₂ is:
When a spinning top is precessing, the torque causing precession is provided by:
A solid cylinder rolls up an incline with initial velocity v. The maximum height reached is:
A body is rolling on a surface without slipping. The ratio of its translational KE to rotational KE for a solid sphere is:
According to the theorem of perpendicular axes, for a planar lamina:
A particle of mass m moves in a circle of radius r with speed v. The magnitude of the angular momentum about the centre is:
A ball of mass m is tied to a string of length r and rotated in a horizontal circle. If the speed is doubled, the centripetal force becomes:
A thin uniform rod of mass M and length L has moment of inertia about an axis through one end perpendicular to its length:
A torque of 2 N·m acts on a body of moment of inertia 1 kg·m² for 5 s. Starting from rest, the angular velocity acquired is:
The angular momentum of a body is L. If its moment of inertia is doubled and angular velocity is halved, the new angular momentum will be:
A hollow cylinder and a solid cylinder of same mass and radius roll without slipping down an inclined plane from the same height. Which reaches the bottom first?
A disc of mass M and radius R is rotating with angular velocity ω. Its kinetic energy is:
A rigid body rotates about a fixed axis with a uniform angular acceleration α. If the body starts from rest, the angle θ rotated in time t is:
A particle moves in a circle of radius r. In half a revolution the displacement of the particle is:
The moment of inertia of a uniform solid sphere of mass M and radius R about its diameter is:
Four solid spheres each of diameter √5 cm and mass 0.5 kg are placed with their centres at the corners of a square of side 4 cm. The moment of inertia of the system about the diagonal of the square is N × 10⁻⁴ kg m², then N is:
The figure shows two cones A and B with the condition: hA ρB, RA = RB, mA = mB. Identify the correct statement about their axis of symmetry.
Three point masses m₁, m₂ and m₃ are located at the vertices of an equilateral triangle of side ‘a’. What is the moment of inertia of the system about an axis along the altitude of the triangle passing through m₁?
Two rods of equal mass m and length l lie along the x-axis and y-axis with their center lying at origin. What is the moment of inertia of both about the line x = y:
Four thin uniform rods each of length L and mass M are joined to form a square ABCD. What is the moment of inertia of square about axis along its diagonal BD?
A uniform rod of mass M and length L is pivoted at one end such that it can rotate in a vertical plane. There is negligible friction at the pivot. The free end of the rod is held vertically above the pivot and then released. The angular acceleration
The instantaneous angular position of a point on a rotating wheel is given by the equation θ(t) = 2t³ − 6t². The torque on the wheel becomes zero at:
In the pulley system shown, if radii of the bigger and smaller pulley are 2m and 1m, respectively and the acceleration of the block A is 5 m/s² in the downward direction, the acceleration of block B will be:
A rod AB of mass M and length L is hinged at end A. The rod is kept horizontal by a massless string tied to point B as shown in figure. When string is cut, the initial angular acceleration of the rod is:
The moment of inertia of a uniform semicircular wire of mass m and radius r, about an axis passing through its centre of mass and perpendicular to its plane is: