The rotor of an electric motor has rotational inertia about its central axis. The motor is used to change the orientation of the space probe in which it is mounted. The motor axis is mounted along the central axis of the probe; the probe has rotational inertia role="math" localid="1660985808865" about this axis. Calculate the number of revolutions of the rotor required to turn the probe through about its central axis.
The number of revolutions of the rotor required to turn the probe through about its central axis are .
Using the conservation law of the angular momentum we can find the angle through which the motor is rotated. As in one rotation the motor is rotated through °, we can find the number of revolutions for the angle through which the motor is rotated.
The law of conservation of angular momentum,
The law of conservation of angular momentum gives
So, the no. of revolutions of the rotor is
Therefore, the no. of revolutions of the rotor is .
A cockroach of mass lies on the rim of a uniform disk of mass that can rotate freely about its centre like a merry- go-round. Initially the cockroach and disk rotate together with an angular velocity of Then the cockroach walks halfway to the centre of the disk.
(a) What then is the angular velocity of the cockroach – disk system?
(b) What is the ratio of the new kinetic energy of the system to its initial kinetic energy?
(c) What accounts for the change in the kinetic energy?
At the instant the displacement of a 2.00kg object relative to the origin is , its velocity is
and it is subject to a force (a) Find the acceleration of the object. (b) Find the angular momentum of the object about the origin. (c) Find the torque about the origin acting on the object. (d) Find the angle between the velocity of the object and the force acting on the object.
A 2.0kg particle-like object moves in a plane with velocity components vx = 30m/s and vy = 60m/s as it passes through the point with (x,y) coordinates of (3.0, -4.0)m. Just then, in unit-vector notation, (a) what is its angular momentum relative to the origin and (b) what is its angular momentum relative to the point located at (-2.0, -2.0)m?
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