Tag: physics

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Multiple choice 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

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

  1. Kinetic energy will decrease.

  2. Moment of inertia will decrease.

  3. Angular momentum will increase.

  4. Angular velocity will remain constant.
Reveal answer Fill a bubble to check yourself
B Correct answer
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. 

Multiple choice 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

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 :

  1. moment of inertia

  2. angular momentum

  3. angular velocity

  4. rotational kinetic energy
Reveal answer Fill a bubble to check yourself
A,C,D Correct answer
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.

Multiple choice 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

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?

  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.
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

The change in angular momentum is equal to the impulse of the torque, which is torque multiplied by time (delta L = tau * delta t).

Multiple choice 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

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.

  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 $
Reveal answer Fill a bubble to check yourself
A Correct answer
Multiple choice 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

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

  1. radius

  2. the tangent to the orbit

  3. a line perpendicular to the plane of rotation

  4. none of above
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Angular momentum is defined as the cross product of the position vector and linear momentum. For a mass rotating in a plane, the direction of this vector is determined by the right-hand rule, which is always perpendicular to the plane of rotation.

Multiple choice 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

The angular momentum of a system of particles is conserved 

  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 
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Angular momentum is conserved when the net external torque acting on a system is zero. This is the rotational analog to the conservation of linear momentum, which occurs when the net external force is zero.

Multiple choice 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

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

  1. $100 rpm$

  2. $150 rpm$

  3. $200 rpm$

  4. $250 rpm$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

By conservation of angular momentum, I1 * w1 = I2 * w2. Given I2 = 0.6 * I1 and w1 = 120 rpm, we have 120 * I1 = w2 * 0.6 * I1, which simplifies to w2 = 120 / 0.6 = 200 rpm.

Multiple choice 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

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)

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

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

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

  4. $6\sqrt{ 2} kg m^2s^{-1}$
Reveal answer Fill a bubble to check yourself
C Correct answer
Multiple choice 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

 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 

  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
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

When a ball strikes a rod on a smooth table, there is an impulsive reaction force at the point of contact. Angular momentum is conserved about any point where the net external torque is zero; for the end point, the impulsive reaction force at the pivot (if it were fixed) or the specific geometry makes the calculation valid.

Multiple choice 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

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

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

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

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

  4. $\frac{1}{2} \sqrt {\frac{GM^3 r}{2}}$
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

For two masses M revolving about their center of mass at distance r/2, the orbital velocity v is found from GM^2 / r^2 = M * v^2 / (r/2). Thus v^2 = GM / 2, so v = sqrt(GM / 2). Angular momentum L = M * v * (r/2) = M * sqrt(GM / 2) * (r/2) = (1/2) * sqrt(GM^3 * r^2 / 2) = (1/2) * sqrt(GM^3 * r / 2).