System of Particles and Rotational Motion

A bicycle wheel of radius r = 1.5 m starts from rest and rolls 100 m without slipping in 30 s. Calculate

(a) The number of revolutions the wheel makes,

(b) The number of radians through which it turns,

(c) The average angular velocity.

The moment of inertia of a straight wire about its perpendicular bisector and the moment of inertia of a circular frame about its perpendicular central axis are I₁ and I₂ respectively.

Explain that the moment of inertia is rotational analogue of the mass.

A car wheel is being tested for balance. It is spinning at 750 rpm and the machine then accelerates it to 1500 rpm over a period of 3 s.  What is the angular acceleration.

A skater spins in the counterclockwise direction, as seen from above. In what direction does the vector representing the angular momentum of the skater point.

A ball with moment of inertia of 1.6, mass of 4 kg and radius of 1 m rolls without slipping down an incline which is 10 meters high. What is the speed of the ball when it reaches the bottom of the incline. 

A uniform cylinder of mass 5 kg and radius 0.2 m rolls smoothly over a horizontal surface in a straight line with a velocity of 2 m/s. 

Find 

(i) the speed of the particle situated at the top of the cylinder and 

(ii) kinetic energy of the rolling cylinder.