Test: Kinematic Variables in Rotation - JEE MCQ

Angular acceleration is the rate of change of angular velocity. In three dimensions, it is a pseudo-vector. In SI units, it is measured in radians per second squared (rad/s2), and is usually denoted by the Greek letter alpha (α).

Linear velocity (V) = angular velocity (w) × radius (r)
v = w × r
w = v/r

Second’s hand of a clock completes one turn in one second.i.e 1 revolution per minute

Angular velocity of second’s hand;

ω = 2π/60 = π/30 rad/s

Angular velocity is a pseudovector , with its magnitude measuring the rate of rotation and its direction pointing along the axis of rotation ( perpendicular to radius and velocity vectors ) .

When the man pulls his hands towards chest, the moment of inertia will decrease and due to conservation of angular momentum, angular velocity will increase.

Angle of line relative to a fixed direction is angular position.

When a body performs circular motion it has got two accelerations radial acc. And tangential acc. Radial acc. Is responsible for changing the direction of velocity of body but tangential acc. Is responsible for changing the magnitide of velocity of body. As the body is moving with constant speed so tangential acc. Is zero. As we know that tangential acc. = radius * angular acc. So angular acc.is zero.

 N = n(n – 1)/2 = 6 x (6 – 1)/2 = 15.

As the direction of all the four velocities are the same thus their momentum also have same directions and hence they can be directly added.
Thus total momentum of the system, P = 0.5 x 2 + 0.5 x 4 + 0.5 x 8 + 0.5 x 10
= 1 + 2 + 4 + 5
= 12 kg m /sec

Just like the equations of motion in 1D, we get the equations of motion for rotation.
We know that s = d/t, analogous to it is 
Hence D is the correct answer.