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

Quizzes (5) Questions (134)

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

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

State whether true or false.
A couple can never be replaced by a single force.

  1. True

  2. False
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

A couple is defined as a pair of two equal and opposite parallel forces acting along two different lines. A couple can produce roatation in the body but not the translational motion. A single force can produce translation motion in the body. Thus the given statement is true that a couple can never be replaced by a single force.

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

State whether true or false.
Only a couple can produce pure rotation in a body.

  1. True

  2. False
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

A couple is defined as a pair of two equal and opposite parallel forces acting along two different lines. Since net force acting on the body is zero, so the body is in translatory equilibrium. A couple produces torque which rotates the body. Thus the given statement is true that only a couple can produce pure rotation in a body.

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

While opening a tap with two fingers, the forces applied by the fingers are:

  1. equal in magnitude

  2. parallel to each other

  3. opposite in direction

  4. all the above
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

A couple has to be applied to the tap in order to open it. A couple is the combination of two equal and opposite parallel forces acting at different axes. Thus option D is correct.

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

$ML^2T^{-2}$ is the dimensional formula for

  1. moment of inertia

  2. pressure

  3. elasticity

  4. couple acting on a body
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

$\left[ MOI \right] =\left[ M{ R }^{ 2 } \right] =\left[ { M }^{ 1 }{ L }^{ 2 }{ T }^{ 0 } \right] \ \left[ Pressure \right] =\left[ N/{ M }^{ 2 } \right] =\left[ { M }^{ 1 }{ L }^{ -1 }{ T }^{ -2 } \right] \ \left[ Couple \right] =\left[ N.{ M } \right] =\left[ { M }^{ 1 }{ L }^{ 2 }{ T }^{ -2 } \right] $

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

An automobile engine develops $100$ $kW$ when rotating at a speed of $1800\ rev/min$. The torque it delivers is

  1. $3.33\ N-m$

  2. $200\ N-m$

  3. $530.5\ N-m$

  4. $2487\ N-m$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

$Power\quad P=100kW\quad =100000W\ w=1800\times \cfrac { 2\pi  }{ 60 } \quad rad/s\ \quad =60\pi \quad rad/s\ P=torque\times w\ torque=530.5\quad Nm$

Multiple choice physics rotational motion of a rigid body and moment of inertia constant angular acceleration equation of motion of rotating body dynamics of rotational motion about a fixed axis

A solid sphere of mass 0.5 kg and diameter 1 m rolls without sliding with a constant velocity of 5 m/s, the ratio of the rotational K.E. to the total kinetic energy of the sphere is :

  1. $\cfrac{7}{10}$

  2. $\cfrac{4}{9}$

  3. $\cfrac{2}{7}$

  4. $\cfrac{1}{2}$
Reveal answer Fill a bubble to check yourself
B Correct answer
Multiple choice physics rotational motion of a rigid body and moment of inertia constant angular acceleration equation of motion of rotating body dynamics of rotational motion about a fixed axis

Newton's second law of motion and work done in rotation of a rigid body can be expressed as 

  1. Newton's law cannot be expressed in rotation, work done in rotation is $W=\tau \ theta$

  2. Force and work done are expressed as $\tau = I \alpha$ and $W=\tau \ theta$

  3. Force can be expressed as $\tau = I \alpha$, while work done will be zero

  4. Force will be zero, since no net displacement is present
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Newton's second law of motion in kinematics is F =  ma. To express the same in rotation, replace mass by moment of inertia I AND linear acceleration a by angular acceleration $\alpha$. Thus, Newton's law of motion becomes, Torque $\tau = I \alpha$

Similarly work done in kinematics is given by W = F.S. To express the same in rotation, replace Force by torque $\tau$ AND linear displacement by angular displacement $\theta$. Thus, Work done becomes, Torque $W= \tau \theta$

Multiple choice physics rotational motion of a rigid body and moment of inertia constant angular acceleration equation of motion of rotating body dynamics of rotational motion about a fixed axis

How do you express Newton's second law of motion in differential form

  1. $\tau=dL/dt$

  2. $\tau=dp/dt$

  3. $\tau=mdv/dt$

  4. $\tau=md\alpha/dt$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Newton's second law for rotation states that the net torque acting on an object is equal to the rate of change of its angular momentum, expressed as tau = dL/dt.