Angular Momentum and its Conservation for a Rigid Body
PHXI07:SYSTEMS OF PARTICLES AND ROTATIONAL MOTION

365658 A person, with outstretched arms, is spinning on a rotating stool. He suddenly brings his arms down to his sides. Which the following is true about his kinetic energy \(K\) and angular momentum \(L\) ?

1 Both \(K\) and \(L\) increase
2 Both \(K\) and \(L\) remain unchanged
3 \(K\) remains constant, \(L\) increases
4 \(K\) increases but \(L\) remains constant
PHXI07:SYSTEMS OF PARTICLES AND ROTATIONAL MOTION

365659 A disc of moment of interia \('{I_1}'\) is rotating in horizontal plane about an axis passing through its centre and perpendicular to its plane with constant angular speed \('{\omega _1}'\). Another disc of moment of interia \('{I_2}'\) having zero angular speed is placed co - axially on a rotating disc. Now, both the discs are rotating with constant angular speed \('{\omega _2}'\). The energy lost by the initial rotating disc is

1 \(\dfrac{1}{2}\left[\dfrac{I_{1}+I_{2}}{I_{1} I_{2}}\right] \omega_{1}^{2}\)
2 \(\dfrac{1}{2}\left[\dfrac{I_{1} I_{2}}{I_{1}-I_{2}}\right] \omega_{1}^{2}\)
3 \(\dfrac{1}{2}\left[\dfrac{I_{1}-I_{2}}{I_{1} I_{2}}\right] \omega_{1}^{2}\)
4 \(\dfrac{1}{2}\left[\dfrac{I_{1} I_{2}}{I_{1}+I_{2}}\right] \omega_{1}^{2}\)
PHXI07:SYSTEMS OF PARTICLES AND ROTATIONAL MOTION

365660 A disc is rotating with an angular speed of \(\omega\). If a child sits on it, which of the following is conserved?

1 Potential energy
2 Kinetic energy
3 Linear momentum
4 Angular momentum
PHXI07:SYSTEMS OF PARTICLES AND ROTATIONAL MOTION

365661 Assertion :
When moment of inertia of a rotating body changes, its angular momentum remain conserved, (in the absence of external torque) but its kinetic energy changes.
Reason :
Angular momentum does not depend upon moment of inertia of the body.

1 Both Assertion and Reason are correct and Reason is the correct explanation of the Assertion.
2 Both Assertion and Reason are correct but Reason is not the correct explanation of the Assertion.
3 Assertion is correct but Reason is incorrect.
4 Assertion is incorrect but reason is correct.
PHXI07:SYSTEMS OF PARTICLES AND ROTATIONAL MOTION

365662 A disc of mass ' \(m\) ' and radius ' \(R\) ' is free to rotate in a horizontal plane about a vertical smooth fixed axis passing through its centre. There is a smooth groove along the diameter of the disc and two small balls of mass \(m/2\) each are placed in it on either side of the centre of the disc as shown in the figure. The disc is given an initial angular velocity \(\omega_{0}\) and released.
The angular speed of the disc when the balls reach the end of the disc is
supporting img

1 \(\dfrac{\omega_{0}}{2}\)
2 \(\dfrac{\omega_{0}}{4}\)
3 \(\dfrac{\omega_{0}}{3}\)
4 \(\dfrac{2 \omega_{0}}{3}\)
PHXI07:SYSTEMS OF PARTICLES AND ROTATIONAL MOTION

365658 A person, with outstretched arms, is spinning on a rotating stool. He suddenly brings his arms down to his sides. Which the following is true about his kinetic energy \(K\) and angular momentum \(L\) ?

1 Both \(K\) and \(L\) increase
2 Both \(K\) and \(L\) remain unchanged
3 \(K\) remains constant, \(L\) increases
4 \(K\) increases but \(L\) remains constant
PHXI07:SYSTEMS OF PARTICLES AND ROTATIONAL MOTION

365659 A disc of moment of interia \('{I_1}'\) is rotating in horizontal plane about an axis passing through its centre and perpendicular to its plane with constant angular speed \('{\omega _1}'\). Another disc of moment of interia \('{I_2}'\) having zero angular speed is placed co - axially on a rotating disc. Now, both the discs are rotating with constant angular speed \('{\omega _2}'\). The energy lost by the initial rotating disc is

1 \(\dfrac{1}{2}\left[\dfrac{I_{1}+I_{2}}{I_{1} I_{2}}\right] \omega_{1}^{2}\)
2 \(\dfrac{1}{2}\left[\dfrac{I_{1} I_{2}}{I_{1}-I_{2}}\right] \omega_{1}^{2}\)
3 \(\dfrac{1}{2}\left[\dfrac{I_{1}-I_{2}}{I_{1} I_{2}}\right] \omega_{1}^{2}\)
4 \(\dfrac{1}{2}\left[\dfrac{I_{1} I_{2}}{I_{1}+I_{2}}\right] \omega_{1}^{2}\)
PHXI07:SYSTEMS OF PARTICLES AND ROTATIONAL MOTION

365660 A disc is rotating with an angular speed of \(\omega\). If a child sits on it, which of the following is conserved?

1 Potential energy
2 Kinetic energy
3 Linear momentum
4 Angular momentum
PHXI07:SYSTEMS OF PARTICLES AND ROTATIONAL MOTION

365661 Assertion :
When moment of inertia of a rotating body changes, its angular momentum remain conserved, (in the absence of external torque) but its kinetic energy changes.
Reason :
Angular momentum does not depend upon moment of inertia of the body.

1 Both Assertion and Reason are correct and Reason is the correct explanation of the Assertion.
2 Both Assertion and Reason are correct but Reason is not the correct explanation of the Assertion.
3 Assertion is correct but Reason is incorrect.
4 Assertion is incorrect but reason is correct.
PHXI07:SYSTEMS OF PARTICLES AND ROTATIONAL MOTION

365662 A disc of mass ' \(m\) ' and radius ' \(R\) ' is free to rotate in a horizontal plane about a vertical smooth fixed axis passing through its centre. There is a smooth groove along the diameter of the disc and two small balls of mass \(m/2\) each are placed in it on either side of the centre of the disc as shown in the figure. The disc is given an initial angular velocity \(\omega_{0}\) and released.
The angular speed of the disc when the balls reach the end of the disc is
supporting img

1 \(\dfrac{\omega_{0}}{2}\)
2 \(\dfrac{\omega_{0}}{4}\)
3 \(\dfrac{\omega_{0}}{3}\)
4 \(\dfrac{2 \omega_{0}}{3}\)
PHXI07:SYSTEMS OF PARTICLES AND ROTATIONAL MOTION

365658 A person, with outstretched arms, is spinning on a rotating stool. He suddenly brings his arms down to his sides. Which the following is true about his kinetic energy \(K\) and angular momentum \(L\) ?

1 Both \(K\) and \(L\) increase
2 Both \(K\) and \(L\) remain unchanged
3 \(K\) remains constant, \(L\) increases
4 \(K\) increases but \(L\) remains constant
PHXI07:SYSTEMS OF PARTICLES AND ROTATIONAL MOTION

365659 A disc of moment of interia \('{I_1}'\) is rotating in horizontal plane about an axis passing through its centre and perpendicular to its plane with constant angular speed \('{\omega _1}'\). Another disc of moment of interia \('{I_2}'\) having zero angular speed is placed co - axially on a rotating disc. Now, both the discs are rotating with constant angular speed \('{\omega _2}'\). The energy lost by the initial rotating disc is

1 \(\dfrac{1}{2}\left[\dfrac{I_{1}+I_{2}}{I_{1} I_{2}}\right] \omega_{1}^{2}\)
2 \(\dfrac{1}{2}\left[\dfrac{I_{1} I_{2}}{I_{1}-I_{2}}\right] \omega_{1}^{2}\)
3 \(\dfrac{1}{2}\left[\dfrac{I_{1}-I_{2}}{I_{1} I_{2}}\right] \omega_{1}^{2}\)
4 \(\dfrac{1}{2}\left[\dfrac{I_{1} I_{2}}{I_{1}+I_{2}}\right] \omega_{1}^{2}\)
PHXI07:SYSTEMS OF PARTICLES AND ROTATIONAL MOTION

365660 A disc is rotating with an angular speed of \(\omega\). If a child sits on it, which of the following is conserved?

1 Potential energy
2 Kinetic energy
3 Linear momentum
4 Angular momentum
PHXI07:SYSTEMS OF PARTICLES AND ROTATIONAL MOTION

365661 Assertion :
When moment of inertia of a rotating body changes, its angular momentum remain conserved, (in the absence of external torque) but its kinetic energy changes.
Reason :
Angular momentum does not depend upon moment of inertia of the body.

1 Both Assertion and Reason are correct and Reason is the correct explanation of the Assertion.
2 Both Assertion and Reason are correct but Reason is not the correct explanation of the Assertion.
3 Assertion is correct but Reason is incorrect.
4 Assertion is incorrect but reason is correct.
PHXI07:SYSTEMS OF PARTICLES AND ROTATIONAL MOTION

365662 A disc of mass ' \(m\) ' and radius ' \(R\) ' is free to rotate in a horizontal plane about a vertical smooth fixed axis passing through its centre. There is a smooth groove along the diameter of the disc and two small balls of mass \(m/2\) each are placed in it on either side of the centre of the disc as shown in the figure. The disc is given an initial angular velocity \(\omega_{0}\) and released.
The angular speed of the disc when the balls reach the end of the disc is
supporting img

1 \(\dfrac{\omega_{0}}{2}\)
2 \(\dfrac{\omega_{0}}{4}\)
3 \(\dfrac{\omega_{0}}{3}\)
4 \(\dfrac{2 \omega_{0}}{3}\)
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PHXI07:SYSTEMS OF PARTICLES AND ROTATIONAL MOTION

365658 A person, with outstretched arms, is spinning on a rotating stool. He suddenly brings his arms down to his sides. Which the following is true about his kinetic energy \(K\) and angular momentum \(L\) ?

1 Both \(K\) and \(L\) increase
2 Both \(K\) and \(L\) remain unchanged
3 \(K\) remains constant, \(L\) increases
4 \(K\) increases but \(L\) remains constant
PHXI07:SYSTEMS OF PARTICLES AND ROTATIONAL MOTION

365659 A disc of moment of interia \('{I_1}'\) is rotating in horizontal plane about an axis passing through its centre and perpendicular to its plane with constant angular speed \('{\omega _1}'\). Another disc of moment of interia \('{I_2}'\) having zero angular speed is placed co - axially on a rotating disc. Now, both the discs are rotating with constant angular speed \('{\omega _2}'\). The energy lost by the initial rotating disc is

1 \(\dfrac{1}{2}\left[\dfrac{I_{1}+I_{2}}{I_{1} I_{2}}\right] \omega_{1}^{2}\)
2 \(\dfrac{1}{2}\left[\dfrac{I_{1} I_{2}}{I_{1}-I_{2}}\right] \omega_{1}^{2}\)
3 \(\dfrac{1}{2}\left[\dfrac{I_{1}-I_{2}}{I_{1} I_{2}}\right] \omega_{1}^{2}\)
4 \(\dfrac{1}{2}\left[\dfrac{I_{1} I_{2}}{I_{1}+I_{2}}\right] \omega_{1}^{2}\)
PHXI07:SYSTEMS OF PARTICLES AND ROTATIONAL MOTION

365660 A disc is rotating with an angular speed of \(\omega\). If a child sits on it, which of the following is conserved?

1 Potential energy
2 Kinetic energy
3 Linear momentum
4 Angular momentum
PHXI07:SYSTEMS OF PARTICLES AND ROTATIONAL MOTION

365661 Assertion :
When moment of inertia of a rotating body changes, its angular momentum remain conserved, (in the absence of external torque) but its kinetic energy changes.
Reason :
Angular momentum does not depend upon moment of inertia of the body.

1 Both Assertion and Reason are correct and Reason is the correct explanation of the Assertion.
2 Both Assertion and Reason are correct but Reason is not the correct explanation of the Assertion.
3 Assertion is correct but Reason is incorrect.
4 Assertion is incorrect but reason is correct.
PHXI07:SYSTEMS OF PARTICLES AND ROTATIONAL MOTION

365662 A disc of mass ' \(m\) ' and radius ' \(R\) ' is free to rotate in a horizontal plane about a vertical smooth fixed axis passing through its centre. There is a smooth groove along the diameter of the disc and two small balls of mass \(m/2\) each are placed in it on either side of the centre of the disc as shown in the figure. The disc is given an initial angular velocity \(\omega_{0}\) and released.
The angular speed of the disc when the balls reach the end of the disc is
supporting img

1 \(\dfrac{\omega_{0}}{2}\)
2 \(\dfrac{\omega_{0}}{4}\)
3 \(\dfrac{\omega_{0}}{3}\)
4 \(\dfrac{2 \omega_{0}}{3}\)
PHXI07:SYSTEMS OF PARTICLES AND ROTATIONAL MOTION

365658 A person, with outstretched arms, is spinning on a rotating stool. He suddenly brings his arms down to his sides. Which the following is true about his kinetic energy \(K\) and angular momentum \(L\) ?

1 Both \(K\) and \(L\) increase
2 Both \(K\) and \(L\) remain unchanged
3 \(K\) remains constant, \(L\) increases
4 \(K\) increases but \(L\) remains constant
PHXI07:SYSTEMS OF PARTICLES AND ROTATIONAL MOTION

365659 A disc of moment of interia \('{I_1}'\) is rotating in horizontal plane about an axis passing through its centre and perpendicular to its plane with constant angular speed \('{\omega _1}'\). Another disc of moment of interia \('{I_2}'\) having zero angular speed is placed co - axially on a rotating disc. Now, both the discs are rotating with constant angular speed \('{\omega _2}'\). The energy lost by the initial rotating disc is

1 \(\dfrac{1}{2}\left[\dfrac{I_{1}+I_{2}}{I_{1} I_{2}}\right] \omega_{1}^{2}\)
2 \(\dfrac{1}{2}\left[\dfrac{I_{1} I_{2}}{I_{1}-I_{2}}\right] \omega_{1}^{2}\)
3 \(\dfrac{1}{2}\left[\dfrac{I_{1}-I_{2}}{I_{1} I_{2}}\right] \omega_{1}^{2}\)
4 \(\dfrac{1}{2}\left[\dfrac{I_{1} I_{2}}{I_{1}+I_{2}}\right] \omega_{1}^{2}\)
PHXI07:SYSTEMS OF PARTICLES AND ROTATIONAL MOTION

365660 A disc is rotating with an angular speed of \(\omega\). If a child sits on it, which of the following is conserved?

1 Potential energy
2 Kinetic energy
3 Linear momentum
4 Angular momentum
PHXI07:SYSTEMS OF PARTICLES AND ROTATIONAL MOTION

365661 Assertion :
When moment of inertia of a rotating body changes, its angular momentum remain conserved, (in the absence of external torque) but its kinetic energy changes.
Reason :
Angular momentum does not depend upon moment of inertia of the body.

1 Both Assertion and Reason are correct and Reason is the correct explanation of the Assertion.
2 Both Assertion and Reason are correct but Reason is not the correct explanation of the Assertion.
3 Assertion is correct but Reason is incorrect.
4 Assertion is incorrect but reason is correct.
PHXI07:SYSTEMS OF PARTICLES AND ROTATIONAL MOTION

365662 A disc of mass ' \(m\) ' and radius ' \(R\) ' is free to rotate in a horizontal plane about a vertical smooth fixed axis passing through its centre. There is a smooth groove along the diameter of the disc and two small balls of mass \(m/2\) each are placed in it on either side of the centre of the disc as shown in the figure. The disc is given an initial angular velocity \(\omega_{0}\) and released.
The angular speed of the disc when the balls reach the end of the disc is
supporting img

1 \(\dfrac{\omega_{0}}{2}\)
2 \(\dfrac{\omega_{0}}{4}\)
3 \(\dfrac{\omega_{0}}{3}\)
4 \(\dfrac{2 \omega_{0}}{3}\)