Question

If 2kg mass is rotating on a circular path of radius 0.8m with angular velocity of 44 rad/sec. If the radius of the path becomes 1m then what will be the value of angular velocity?
A. 28.16 rad/sec
B. 19.28 rad/sec
C. 8.12 rad/sec
D. 35.26 rad/sec

Answer 1

Hint: We need to use the fact that the angular momentum of the given mass will remain the same when the radius of the path changes. By equating the expression for angular momentum for the two cases, we can get the required value of angular velocity.
Formula used:
The angular momentum of a mass m moving in a circular path of radius r with angular velocity $\omega $ is given as
$L = m\omega {r^2}$

Complete answer:
We are given an object whose mass is
$m = 2kg$
It is rotating on a circular path whose radius is given as
${r_1} = 0.8m$
The angular velocity of this mass is given as
${\omega _1} = 44rad/s$
Now the radius of the path increases and is given as
${r_2} = 1m$
Now we need to remember that the angular momentum of the given mass will be the same as the radius of the path is increased. The angular momentum of a mass m is given as
$L = m\omega {r^2}$
Now this will be the same in the two cases that we have. Therefore we can write
$
  m{\omega _1}r_1^2 = m{\omega _2}r_2^2 \\
  {\omega _1}r_1^2 = {\omega _2}r_2^2 \\
  {\omega _2} = \dfrac{{r_1^2}}{{r_2^2}}{\omega _1} \\
 $
Here ${\omega _2}$ is the angular velocity that we are asked to find out. Now we can insert the known values in the above expression. Doing so, we get
${\omega _2} = {\left( {\dfrac{{0.8}}{1}} \right)^2} \times 44 = 28.16rad/s$

So, the correct answer is “Option A”.

Note:
The angular momentum can also be defined as the product of the moment of inertia of the given mass and the angular velocity of the given mass. The moment of inertia is equal to the product of mass of the object and the square of the radius of the path and we finally get the expression that we have used for angular momentum in the solution.