Advertisements
Advertisements
प्रश्न
A diver having a moment of inertia of 6⋅0 kg-m2 about an axis thorough its centre of mass rotates at an angular speed of 2 rad/s about this axis. If he folds his hands and feet to decrease the moment of inertia to 5⋅0 kg-m2, what will be the new angular speed?
Advertisements
उत्तर
Initial moment of inertia of diver, I1 = 6 kg-m2
Initial angular velocity of diver, ω1 = 2 rad/s
Final moment of inertia of diver, I2 = 5 kg-m2
Let ω2 be the final angular velocity of the diver.
We have
External torque = 0
∴ I1ω1 = I2ω2
\[\Rightarrow \omega_2 = \frac{6 \times 2}{5} = 2.4 \text{ rad/s}\]
APPEARS IN
संबंधित प्रश्न
Torques of equal magnitude are applied to a hollow cylinder and a solid sphere, both having the same mass and radius. The cylinder is free to rotate about its standard axis of symmetry, and the sphere is free to rotate about an axis passing through its centre. Which of the two will acquire a greater angular speed after a given time?
Torques of equal magnitude are applied to a hollow cylinder and a solid sphere, both having the same mass and radius. The cylinder is free to rotate about its standard axis of symmetry, and the sphere is free to rotate about an axis passing through its centre. Which of the two will acquire a greater angular speed after a given time?
A hoop of radius 2 m weighs 100 kg. It rolls along a horizontal floor so that its centre of mass has a speed of 20 cm/s. How much work has to be done to stop it?
The oxygen molecule has a mass of 5.30 × 10–26 kg and a moment of inertia of 1.94×10–46 kg m2 about an axis through its centre perpendicular to the lines joining the two atoms. Suppose the mean speed of such a molecule in a gas is 500 m/s and that its kinetic energy of rotation is two thirds of its kinetic energy of translation. Find the average angular velocity of the molecule.
Two discs of moments of inertia I1 and I2 about their respective axes (normal to the disc and passing through the centre), and rotating with angular speeds ω1 and ω2 are brought into contact face to face with their axes of rotation coincident. (a) What is the angular speed of the two-disc system? (b) Show that the kinetic energy of the combined system is less than the sum of the initial kinetic energies of the two discs. How do you account for this loss in energy? Take ω1 ≠ ω2.
A cylinder of mass 10 kg and radius 15 cm is rolling perfectly on a plane of inclination 30°. The coefficient of static friction µs = 0.25.
(a) How much is the force of friction acting on the cylinder?
(b) What is the work done against friction during rolling?
(c) If the inclination θ of the plane is increased, at what value of θ does the cylinder begin to skid, and not roll perfectly?
The moment of inertia of a uniform semicircular wire of mass M and radius r about a line perpendicular to the plane of the wire through the centre is ___________ .
Let I1 an I2 be the moments of inertia of two bodies of identical geometrical shape, the first made of aluminium and the second of iron.
A string is wrapped on a wheel of moment of inertia 0⋅20 kg-m2 and radius 10 cm and goes through a light pulley to support a block of mass 2⋅0 kg as shown in the following figure. Find the acceleration of the block.
The pulley shown in the following figure has a radius 10 cm and moment of inertia 0⋅5 kg-m2about its axis. Assuming the inclined planes to be frictionless, calculate the acceleration of the 4⋅0 kg block.
Solve the previous problem if the friction coefficient between the 2⋅0 kg block and the plane below it is 0⋅5 and the plane below the 4⋅0 kg block is frictionless.
A uniform metre stick of mass 200 g is suspended from the ceiling thorough two vertical strings of equal lengths fixed at the ends. A small object of mass 20 g is placed on the stick at a distance of 70 cm from the left end. Find the tensions in the two strings.
A wheel of moment of inertia 0⋅500 kg-m2 and radius 20⋅0 cm is rotating about its axis at an angular speed of 20⋅0 rad/s. It picks up a stationary particle of mass 200 g at its edge. Find the new angular speed of the wheel.
A boy is seated in a revolving chair revolving at an angular speed of 120 revolutions per minute. Two heavy balls form part of the revolving system and the boy can pull the balls closer to himself or may push them apart. If by pulling the balls closer, the boy decreases the moment of inertia of the system from 6 kg-m2 to 2 kg-m2, what will be the new angular speed?
Two blocks of masses 400 g and 200 g are connected through a light string going over a pulley which is free to rotate about its axis. The pulley has a moment of inertia \[1 \cdot 6 \times {10}^{- 4} kg - m^2\] and a radius 2⋅0 cm, Find (a) the kinetic energy of the system as the 400 g block falls through 50 cm, (b) the speed of the blocks at this instant.
A wheel of mass 15 kg has a moment of inertia of 200 kg-m2 about its own axis, the radius of gyration will be:
A uniform square plate has a small piece Q of an irregular shape removed and glued to the centre of the plate leaving a hole behind (Figure). The moment of inertia about the z-axis is then ______.
Four equal masses, m each are placed at the corners of a square of length (l) as shown in the figure. The moment of inertia of the system about an axis passing through A and parallel to DB would be ______.
