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

365684 A man sits on a freely rotating stool holding two dumbbells, each of mass \(2.0\,kg\). When his arms are extended horizontally [Fig. (a)], the dumbbells are \(1.0\,m\) from the axis of rotation and the man rotates with an angular speed of \(0.50\,rad/s\). The moment of inertia of the man plus stool is \({5.0 {~kg} \cdot {m}^{2}}\) and is assumed to be constant. The man pulls the dumbbells inward horizontally to a position \(0.50\,m\) from the rotation axis [Fig. (b)]. Find the new angular speed of the man
supporting img

1 \(0.90\,rad/s\)
2 \(0.67\,rad/s\)
3 \(0.45\,rad/s\)
4 \(0.15\,rad/s\)
PHXI07:SYSTEMS OF PARTICLES AND ROTATIONAL MOTION

365685 When acrobat bends his body (assume no external torque)
supporting img

1 \(I_{\text {acrobat }}\) decrease
2 \(I_{\text {acrobat }}\) will increase
3 \(\omega_{\text {acrobat }}\) increase
4 Both (1) and (3)
PHXI07:SYSTEMS OF PARTICLES AND ROTATIONAL MOTION

365686 Statement A :
If the total force on the body is zero, then the total linear momentum of the body does not change with time.
Statement B :
If the total torque on the rigid body is zero, the total angular momentum of the body does not change with time.

1 Statement A is correct but Statement B is incorrect.
2 Statement A is incorrect but Statement B is correct.
3 Both statements are correct.
4 Both Statements are incorrect.
PHXI07:SYSTEMS OF PARTICLES AND ROTATIONAL MOTION

365687 A thin circular ring of mass \(M\) is rotating about its axis with a constant angular velocity \(\omega\). Two objects, each of mass \(m\), are attached gently to the opposite ends of a diameter of the ring. The ring now rotates with an angular velocity:

1 \(\dfrac{\omega(M-2 m)}{M-2 m}\)
2 \(\dfrac{\omega M}{M-m}\)
3 \(\dfrac{\omega(M+2 m)}{M}\)
4 \(\dfrac{M \omega}{M+2 m}\)
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PHXI07:SYSTEMS OF PARTICLES AND ROTATIONAL MOTION

365684 A man sits on a freely rotating stool holding two dumbbells, each of mass \(2.0\,kg\). When his arms are extended horizontally [Fig. (a)], the dumbbells are \(1.0\,m\) from the axis of rotation and the man rotates with an angular speed of \(0.50\,rad/s\). The moment of inertia of the man plus stool is \({5.0 {~kg} \cdot {m}^{2}}\) and is assumed to be constant. The man pulls the dumbbells inward horizontally to a position \(0.50\,m\) from the rotation axis [Fig. (b)]. Find the new angular speed of the man
supporting img

1 \(0.90\,rad/s\)
2 \(0.67\,rad/s\)
3 \(0.45\,rad/s\)
4 \(0.15\,rad/s\)
PHXI07:SYSTEMS OF PARTICLES AND ROTATIONAL MOTION

365685 When acrobat bends his body (assume no external torque)
supporting img

1 \(I_{\text {acrobat }}\) decrease
2 \(I_{\text {acrobat }}\) will increase
3 \(\omega_{\text {acrobat }}\) increase
4 Both (1) and (3)
PHXI07:SYSTEMS OF PARTICLES AND ROTATIONAL MOTION

365686 Statement A :
If the total force on the body is zero, then the total linear momentum of the body does not change with time.
Statement B :
If the total torque on the rigid body is zero, the total angular momentum of the body does not change with time.

1 Statement A is correct but Statement B is incorrect.
2 Statement A is incorrect but Statement B is correct.
3 Both statements are correct.
4 Both Statements are incorrect.
PHXI07:SYSTEMS OF PARTICLES AND ROTATIONAL MOTION

365687 A thin circular ring of mass \(M\) is rotating about its axis with a constant angular velocity \(\omega\). Two objects, each of mass \(m\), are attached gently to the opposite ends of a diameter of the ring. The ring now rotates with an angular velocity:

1 \(\dfrac{\omega(M-2 m)}{M-2 m}\)
2 \(\dfrac{\omega M}{M-m}\)
3 \(\dfrac{\omega(M+2 m)}{M}\)
4 \(\dfrac{M \omega}{M+2 m}\)
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PHXI07:SYSTEMS OF PARTICLES AND ROTATIONAL MOTION

365684 A man sits on a freely rotating stool holding two dumbbells, each of mass \(2.0\,kg\). When his arms are extended horizontally [Fig. (a)], the dumbbells are \(1.0\,m\) from the axis of rotation and the man rotates with an angular speed of \(0.50\,rad/s\). The moment of inertia of the man plus stool is \({5.0 {~kg} \cdot {m}^{2}}\) and is assumed to be constant. The man pulls the dumbbells inward horizontally to a position \(0.50\,m\) from the rotation axis [Fig. (b)]. Find the new angular speed of the man
supporting img

1 \(0.90\,rad/s\)
2 \(0.67\,rad/s\)
3 \(0.45\,rad/s\)
4 \(0.15\,rad/s\)
PHXI07:SYSTEMS OF PARTICLES AND ROTATIONAL MOTION

365685 When acrobat bends his body (assume no external torque)
supporting img

1 \(I_{\text {acrobat }}\) decrease
2 \(I_{\text {acrobat }}\) will increase
3 \(\omega_{\text {acrobat }}\) increase
4 Both (1) and (3)
PHXI07:SYSTEMS OF PARTICLES AND ROTATIONAL MOTION

365686 Statement A :
If the total force on the body is zero, then the total linear momentum of the body does not change with time.
Statement B :
If the total torque on the rigid body is zero, the total angular momentum of the body does not change with time.

1 Statement A is correct but Statement B is incorrect.
2 Statement A is incorrect but Statement B is correct.
3 Both statements are correct.
4 Both Statements are incorrect.
PHXI07:SYSTEMS OF PARTICLES AND ROTATIONAL MOTION

365687 A thin circular ring of mass \(M\) is rotating about its axis with a constant angular velocity \(\omega\). Two objects, each of mass \(m\), are attached gently to the opposite ends of a diameter of the ring. The ring now rotates with an angular velocity:

1 \(\dfrac{\omega(M-2 m)}{M-2 m}\)
2 \(\dfrac{\omega M}{M-m}\)
3 \(\dfrac{\omega(M+2 m)}{M}\)
4 \(\dfrac{M \omega}{M+2 m}\)
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PHXI07:SYSTEMS OF PARTICLES AND ROTATIONAL MOTION

365684 A man sits on a freely rotating stool holding two dumbbells, each of mass \(2.0\,kg\). When his arms are extended horizontally [Fig. (a)], the dumbbells are \(1.0\,m\) from the axis of rotation and the man rotates with an angular speed of \(0.50\,rad/s\). The moment of inertia of the man plus stool is \({5.0 {~kg} \cdot {m}^{2}}\) and is assumed to be constant. The man pulls the dumbbells inward horizontally to a position \(0.50\,m\) from the rotation axis [Fig. (b)]. Find the new angular speed of the man
supporting img

1 \(0.90\,rad/s\)
2 \(0.67\,rad/s\)
3 \(0.45\,rad/s\)
4 \(0.15\,rad/s\)
PHXI07:SYSTEMS OF PARTICLES AND ROTATIONAL MOTION

365685 When acrobat bends his body (assume no external torque)
supporting img

1 \(I_{\text {acrobat }}\) decrease
2 \(I_{\text {acrobat }}\) will increase
3 \(\omega_{\text {acrobat }}\) increase
4 Both (1) and (3)
PHXI07:SYSTEMS OF PARTICLES AND ROTATIONAL MOTION

365686 Statement A :
If the total force on the body is zero, then the total linear momentum of the body does not change with time.
Statement B :
If the total torque on the rigid body is zero, the total angular momentum of the body does not change with time.

1 Statement A is correct but Statement B is incorrect.
2 Statement A is incorrect but Statement B is correct.
3 Both statements are correct.
4 Both Statements are incorrect.
PHXI07:SYSTEMS OF PARTICLES AND ROTATIONAL MOTION

365687 A thin circular ring of mass \(M\) is rotating about its axis with a constant angular velocity \(\omega\). Two objects, each of mass \(m\), are attached gently to the opposite ends of a diameter of the ring. The ring now rotates with an angular velocity:

1 \(\dfrac{\omega(M-2 m)}{M-2 m}\)
2 \(\dfrac{\omega M}{M-m}\)
3 \(\dfrac{\omega(M+2 m)}{M}\)
4 \(\dfrac{M \omega}{M+2 m}\)
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