A circular disc is rotating about its own axis. An external opposing torque 0.02 Nm is applied on the disc by which it comes rest in 5 seconds. The initial angular momentum of disc is
- $0.1\,kgm^2s^{-1}$
- $0.04\,kgm^2s^{-1}$
- $0.025\,kgm^2s^{-1}$
- $0.01\,kgm^2s^{-1}$
The Correct Option is A
Approach Solution - 1
Rate of change of angular momentum is equal to the torque:
\(\tau=\frac {dL}{dt}\)
\(\tau= \frac {(L_f-L_i)}{△ t}\)
Where,
\(L_f\)= Finial angular momentum
\(L_i\)= Initial angular momentum.
As external force is mentioned, therefore we can say the torque is retarding which will be in negative.
\(-0.02\ Nm=\frac {0-Li}{5}\)
\(0.02\ Nm=\frac {Li-0}{5}\)
\(Li=0.10\ kgm^2s^{-1}\)
So, the correct option is (A): \(0.10\ kgm^2s^{-1}\).
Approach Solution -2
\(C = 0.02\) N/m
\(t = 5\) sec
Torque is applied for \(5 \ sec\) and torque is rate of change of angular momentum
Therefore, angular momentum lost due to decelaration \(= \bar C\times \Delta t = (0.02) \times 5 = 0.1\)
change in angular momentum = final angular momentum - initial angular momentum
\(⇒\) 0.1 = 0 - Initial angular momentum
\(⇒\) Initial angular momentum = \(0.1 \ kg m^2s^{-1}\)
So, the correct option is (A): \(0.1 \ kg m^2s^{-1}\)
Top Questions on momentum
- An object of mass \( m \) is projected from the origin in a vertical \( xy \)-plane at an angle \( 45^\circ \) with the x-axis with an initial velocity \( v_0 \). The magnitude and direction of the angular momentum of the object with respect to the origin, when it reaches the maximum height, will be:
Given below are two statements. One is labelled as Assertion (A) and the other is labelled as Reason (R).
Assertion (A): Knowing the initial position \( x_0 \) and initial momentum \( p_0 \) is enough to determine the position and momentum at any time \( t \) for a simple harmonic motion with a given angular frequency \( \omega \).
Reason (R): The amplitude and phase can be expressed in terms of \( x_0 \) and \( p_0 \).
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Concepts Used:
Momentum
It can be defined as "mass in motion." All objects have mass; so if an object is moving, then it is called as momentum.
the momentum of an object is the product of mass of the object and the velocity of the object.
Momentum = mass • velocity
The above equation can be rewritten as
p = m • v
where m is the mass and v is the velocity.
Momentum is a vector quantity and the direction of the of the vector is the same as the direction that an object.