A flat surface of a thin uniform disk A of radius R is glued to a horizontal table. Another thin uniform disk B of mass M and with the same radius R rolls without slipping on the circumference of A , as shown in the figure. A flat surface of B also lies on the plane of the table. The center of…

Question

A flat surface of a thin uniform disk A of radius R is glued to a horizontal table. Another thin uniform disk B of mass M and with the same radius R rolls without slipping on the circumference of A , as shown in the figure. A flat surface of B also lies on the plane of the table. The center of mass of B has fixed angular speed &omega; about the vertical axis passing through the center of A . The angular momentum of B is n M &omega; R 2 with respect to the center of A . Which of the following is the value of n ? ​​​​​​​

Aicharya · Accepted Answer

The centre of mass of B has angular velocity &#969; about the centre of A . Therefore, the velocity of the centre of B is V B = &#969; 2 R . The point of contact of A and B is at rest therefore, the angular velocity of B will be, &#969; B = v B R = 2 &#969; Now the angular momentum of B with respect to centre of A L = M v B r + I C M &#969; B &#8658; L = M &#969; 2 R 2 R + M R 2 2 2 &#969; L = 5 M R 2 &#969; Comparing the magnitude with n M &#969; R 2 n = 5 `

A flat surface of a thin uniform disk A of radius R is glued to a horizontal table. Another thin uniform…

Solution