Physics Homework Help?

Question

A small mass m attached to the end of a string revolves in a circle on a frictionless tabletop. The other end of the string passes through a hole in the table (the figure (Figure 1) ). Initially, the mass revolves with a speed v1 = 2.3 m/s in a circle of radius r1 = 0.80 m. The string is then pulled slowly through the hole so that the radius is reduced to r2 = 0.48 m.

What is the speed, v2, of the mass now?

 

 

Answer 1

Step 1:

A small mass  attached to the end of a string revolves in a circle on a frictionless tabletop.

The other end of the string passes through a hole in the table.

Initially, the mass revolves with a speed in a circle of radius is .

The string is then pulled slowly through the hole so that the radius is reduced to .

Find the speed .

Initially the angular momentum is .

The angular momentum after reduced the radius is .

The angular momentum is .

Substitute and .

.

Step 2:

Using law of conservative of angular momentum: .

Therefore, .

The mass is constant.

Substitute , and .

.

Solution:

.