Tag: rotational motion of a rigid body and moment of inertia

Questions Related to rotational motion of a rigid body and moment of inertia

If a car is moving forward, what is the direction of the moment of the moment caused by the rotation of the tires

physics forces - vectors and moments the turning of couple couple rotational motion of a rigid body and moment of inertia turning effect of force

  1. It is heading inwards, i.e. the direction is towards inside of the car

  2. It is heading outwards, i.e. the direction is towards outside of the car

  3. It is heading forward, i.e. the direction is towards the forward direction of the motion of the car

  4. It is heading backward, i.e. the direction is towards back side of the motion of the car

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Correct Option: A
Explanation:

Which of the following is/are the properties of moment of a couple?

physics forces - vectors and moments the turning of couple couple rotational motion of a rigid body and moment of inertia turning effect of force

  1. It tends to produce pure rotation.

  2. It is different about any point in the plane of lines of action of the forces.

  3. It can be replaced by any other couple of the same moment.

  4. The resultant of set of two or more couples is equal to the sum of the moments of the individual couples.

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Correct Option: A,C,D
Explanation:

A couple when applied to a body it produce 

(i) Pure rotation
(ii) It can be replaced by any other couple of same moment.
(iii) The resultant of set of two or more couples is equal to the sum of moment of individuals couples.

Two like parallel forces $20\ N$ and $30\ N$ act at the ends $A$ and $B$ of a rod $1.5\ m$ long. The resultant of the forces will act at the point:

physics forces - vectors and moments the turning of couple couple rotational motion of a rigid body and moment of inertia turning effect of force

  1. $90\ cm$ from A

  2. $75\ cm$ from B

  3. $20\ cm$ from B

  4. $85\ cm$ from A

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Correct Option: A
Explanation:

Consider the point at which resultant of the forces will act, is 'x' m from the point A.

Thus the point is (1.5 - x) m far from the point B.

Thus, using the formula Torque = Distance x Force acting

$20x = 30(1.5 - x)$

or,$ 2x = 4.5 - 3x$

or,$ 5x = 4.5$

or, $x = 0.9m or 90cm$

Thus the resultant point will be 0.9 m or 90 cm far from point A

Two small kids weighing 10kg and 15kg are trying to balance a seesaw of total length 5m with the fulcrum at the centre. If one of the kids is sitting at an end, the other should sit at

physics forces - vectors and moments the turning of couple couple rotational motion of a rigid body and moment of inertia turning effect of force

  1. 1.7 m from the centre

  2. 2.5 m from the centre

  3. 2 m from the centre

  4. 1 m from the centre

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Correct Option: A

A couple produces

physics forces - vectors and moments the turning of couple couple rotational motion of a rigid body and moment of inertia turning effect of force

  1. Linear motion

  2. Rotational motion

  3. Both $A$ and $B$

  4. Nether $A$ nor $B$

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Correct Option: B
Explanation:

A couple consists of two parallel forces that are equal in magnitude, opposite in sense and do not share a line of action. It does not produce any translation, but only rotational motion.

A couple is acting on a two particle systems. The resultant motion will be

physics forces - vectors and moments the turning of couple couple rotational motion of a rigid body and moment of inertia turning effect of force

  1. Purely rotational motion

  2. Purely linear motion

  3. Both $A$ and $B$

  4. None of these

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Correct Option: A
Explanation:

A couple consists of two equal and opposite forces whose lines of action are parallel and laterally separated by the some distance. Therefore, net force (or resultant) of a couple is null vector, hence there is no translational acceleration, only rotational motion will be there.

A couple can never be replaced by a single force.

physics forces - vectors and moments the turning of couple couple rotational motion of a rigid body and moment of inertia turning effect of force

  1. True

  2. False

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Correct Option: A
Explanation:

True , because a couple donot  produces any linear acceleration it only produces only rotation but single force will produce linear acceleration too.

so the answer is A.

A couple produces,_____

physics forces - vectors and moments the turning of couple couple rotational motion of a rigid body and moment of inertia turning effect of force

  1. pure rotation

  2. pure translation

  3. rotation and translation

  4. no motion

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Correct Option: A

In case of torque of a couple, if the axis is changed by displacing it parallel to itself, torque will

physics forces - vectors and moments the turning of couple couple rotational motion of a rigid body and moment of inertia turning effect of force

  1. Increase

  2. Decrease

  3. Remain constant

  4. None of these

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Correct Option: C
Explanation:
Torque of a couple   $\tau = d\times F$
where  $d$ is the distance between the two equal force $F$
Thus, the distance between the forces remains the same even on changing the axis. So, the torque will remain the same.

A couple produces :

physics forces - vectors and moments the turning of couple couple rotational motion of a rigid body and moment of inertia turning effect of force

  1. no motion

  2. linear and rotational motion

  3. purely rotational motion

  4. purely linear motion

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Correct Option: C
Explanation:

A couple consists of two equal and opposite forces acting at a separation, so that net force becomes zero. When a couple acts on a body it rotates the body but does not produce any translatory motion. Hence, only rotational motion is produced.