Tag: physics

Questions Related to physics

If a person sitting on a rotating stool with his hands outstretched, suddenly lowers his hands, then his :

physics rotational motion of a rigid body and moment of inertia angular momentum (l) and conservation of angular momentum angular momentum in case of rotation about a fixed axis law of conservation of angular momentum

  1. Kinetic energy will decrease.

  2. Moment of inertia will decrease.

  3. Angular momentum will increase.

  4. Angular velocity will remain constant.

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Correct Option: B
Explanation:

According to conservation of Angular Momentum,
$I \omega$ = constant
Hence, when a person sitting on a rotating stool suddenly  lowers his hands, then his angular velocity will increase and moment of inertia will decrease. 

A man spinning in free space changes the shape of his body, eg. by spreading his arms or curling up. By doing this, he can change his :

physics rotational motion of a rigid body and moment of inertia angular momentum (l) and conservation of angular momentum angular momentum in case of rotation about a fixed axis law of conservation of angular momentum

  1. moment of inertia

  2. angular momentum

  3. angular velocity

  4. rotational kinetic energy

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Correct Option: A,C,D
Explanation:

The moment of inertia can be increased or angular velocity can be decreased by stretching hands outside. Also, smaller the moment of inertia means less resistance to rotation (some rapid corrections have to made to achieve rotational equilibrium), hence change in moment of inertia leads the change in rotational kinetic energy. While angular momentum remains conserved.

Two particles are initially moving with angular momentum $\vec{L _{1}}$ and $\vec{L _{2}}$ in a region of space with no external torque. A constant external torque $\vec{\tau}$ then acts on one particle, but not on the other particle, for a time interval $\Delta{t}$. What is the change in the total angular momentum of the two particles?

physics rotational motion of a rigid body and moment of inertia angular momentum (l) and conservation of angular momentum angular momentum in case of rotation about a fixed axis law of conservation of angular momentum

  1. $\vec\Delta L=\vec {L _{1}}-\vec{L _{2}}$

  2. $\Delta L=\dfrac{1}{2}(\vec {L _{1}}-\vec{L _{2}})$

  3. $\vec\Delta L=\tau \Delta t$

  4. $\vec\Delta L$ is not applicable for this system.

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Correct Option: C

uniform disc of mass M and radius R is rotating about its centre of mass (the centre of mass is at rest )with an angular speed $\omega $.the angular momentum of disc about a point A (as shown)will be.

physics rotational motion of a rigid body and moment of inertia angular momentum (l) and conservation of angular momentum angular momentum in case of rotation about a fixed axis law of conservation of angular momentum

  1. $M{R^2}\omega + MhR\omega $

  2. $\frac{1}{2}M{R^2}\omega $

  3. $\frac{1}{2}M{R^2}\omega + MhR\omega $

  4. $\frac{1}{2}M{R^2}\omega + 1/2MhR\omega $

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Correct Option: A

when a mass is rotating in a plane about a fixed point, its angular momentum is directed along

physics rotational motion of a rigid body and moment of inertia angular momentum (l) and conservation of angular momentum angular momentum in case of rotation about a fixed axis law of conservation of angular momentum

  1. radius

  2. the tangent to the orbit

  3. a line perpendicular to the plane of rotation

  4. none of above

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Correct Option: C

The angular momentum of a system of particles is conserved 

physics rotational motion of a rigid body and moment of inertia angular momentum (l) and conservation of angular momentum angular momentum in case of rotation about a fixed axis law of conservation of angular momentum

  1. When no external force acts upon the system

  2. When no external torque acts upon the system

  3. When no external impulse acts upon the system

  4. none of these 

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Correct Option: B

A ballet dancer spins about a vertical axis at $120 rpm$ with arms stretched with her arms folded the moment of inertia about the axis of rotation decreases by $40\%$ calculate new rate of rotation

physics rotational motion of a rigid body and moment of inertia angular momentum (l) and conservation of angular momentum angular momentum in case of rotation about a fixed axis law of conservation of angular momentum

  1. $100 rpm$

  2. $150 rpm$

  3. $200 rpm$

  4. $250 rpm$

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Correct Option: C

A particle of mass $300 g$ is moving with a speed of $20 ms-1$ along the straight line $y= x-4\sqrt { 2 }$. The angular momentum of the particle about the origin is (where y & x are in metres)

physics rotational motion of a rigid body and moment of inertia angular momentum (l) and conservation of angular momentum angular momentum in case of rotation about a fixed axis law of conservation of angular momentum

  1. $ 24 kg m^2s^{-1}$

  2. $24\sqrt{ 2} kg m^2s^{-1}$

  3. $12 kg m^2s^{-1}$

  4. $6\sqrt{ 2} kg m^2s^{-1}$

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Correct Option: C

 A rod of mass M and length L is placed on a smooth horizontal table and is hit by a ball moving horizontally and perpendicular to length of rod and sticks to it.Then conservation of angular momentum can be applied 

physics rotational motion of a rigid body and moment of inertia angular momentum (l) and conservation of angular momentum angular momentum in case of rotation about a fixed axis law of conservation of angular momentum

  1. About any point on the rod

  2. About a point at the centre of the rod

  3. About end point of the rod

  4. None

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Correct Option: C

Two spherical bodies of equal mass (M) revolve about their centre of mass. The distance between the centre of the two masses is r. The angular momentum of each about their centre of mass is

physics rotational motion of a rigid body and moment of inertia angular momentum (l) and conservation of angular momentum angular momentum in case of rotation about a fixed axis law of conservation of angular momentum

  1. $2 \sqrt {GM^3 r}$

  2. $\frac{1}{2} \sqrt {GM^3 r}$

  3. $\frac{1}{2} \sqrt {2GM^3 r}$

  4. $\frac{1}{2} \sqrt {\frac{GM^3 r}{2}}$

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Correct Option: D