Practice free Rotational Motion (Physics) NEET multiple-choice questions online with instant answers and detailed explanations. No login required.
When considering the equilibrium of a rigid body, the term 'force' refers to:
The NCERT text explicitly states: 'Henceforth we shall omit the adjective 'external' because unless stated otherwise, we shall deal with only external forces and torques.'
Which of the following is true for a rigid body rotating about a fixed axis?
The NCERT summary point 3 states: 'In rotation about a fixed axis, every particle of the rigid body moves in a circle which lies in a plane perpendicular to the axis and has its centre on the axis. Every Point in the rotating rigid body has the same angular velocity at any instant of time.'
A rigid body is subjected to a system of forces. It is observed to be in rotational equilibrium, but not in translational equilibrium. Which of the following conditions correctly describes this situation?
For rotational equilibrium, the total torque must be zero ($\sum \vec{\tau_i} = 0$). For 'not in translational equilibrium', the total force must be non-zero ($\sum \vec{F_i} \neq 0$). This combination corresponds to the description of partial equilibrium provided in the text, specifically the example with Fig. 6.20(a) where the rod was in rotational equilibrium ($net moment = 0$) but not translational equilibrium ($\sum F \neq 0$).
For a rigid body rotating about a fixed axis, which of the following statements is true regarding the angular velocity?
According to the NCERT text, 'In our discussion so far the angular velocity appears to be a scalar. In fact, it is a vector... For rotation about a fixed axis, the angular velocity vector lies along the axis of rotation...'. Therefore, option 3 is correct.
The linear velocity (v) of a particle of a rigid body rotating about a fixed axis is related to its angular velocity ($\omega$) and position vector (r) by which of the following expressions?
The NCERT text states, 'The linear velocity of the particle at P is $\mathbf{v} = \mathbf{\omega} \times \mathbf{r}$.' This vector product correctly represents the relationship between linear and angular velocity.
In the rotation of a rigid body about a fixed axis, every particle of the body moves in a circle. What is the orientation of this circle relative to the axis of rotation?
The NCERT text mentions, 'every particle of the body moves in a circle, which lies in a plane perpendicular to the axis and has its centre on the axis.' This directly answers the question.
For a rigid body rotating about a fixed axis, if the origin is chosen on the axis of rotation, and 'r' is the position vector of a particle P, then where is the center of the circular path of particle P?
The NCERT text states, 'every particle of the body moves in a circle, which lies in a plane perpendicular to the axis and has its centre on the axis.' Since the origin is chosen on the axis, the center of the circle must also be on the axis.
A particle P of a rigid body is rotating about a fixed z-axis. The linear velocity $\mathbf{v}$ of the particle is tangent to the circle described by the particle. What is the relationship between $\mathbf{v}$, $\mathbf{\omega}$ (angular velocity), and $\mathbf{r}$ (position vector from origin on axis)?
The NCERT text states, 'The linear velocity of the particle at P is $\mathbf{v} = \mathbf{\omega} \times \mathbf{r}$. It is perpendicular to both $\mathbf{\omega}$ and $\mathbf{r}$ and is directed along the tangent to the circle described by the particle.' This clarifies that $\mathbf{v}$ is perpendicular to both.
If a rigid body is undergoing pure rotation about a fixed axis, what is common for all particles of the body at any given instant of time?
The NCERT text explicitly states, 'Every Point in the rotating rigid body has the same angular velocity at any instant of time.' and also 'we may characterise pure rotation by all parts of the body having the same angular velocity at any instant of time'.
For particles located on the axis of rotation of a rigid body, what is their linear velocity?
The NCERT text explains, 'For particles on the axis, $r = 0$, and hence $v = \omega r = 0$. Thus, particles on the axis are stationary.'
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