Physics

Rotational and Circular Motion

235 Questions

Rotational and circular motion examines the dynamics of objects moving in circular paths or rotating around an axis. Key concepts include angular momentum, torque, moment of inertia, and centripetal force. This is a highly scoring topic in the physics section of competitive exams.

Angular momentumCentripetal forceMoment of inertiaRolling objectsGyroscopic effect

Rotational and Circular Motion Questions

Multiple choice

A spinning top is slowing down due to friction. What happens to its angular momentum?

  1. It increases

  2. It remains the same

  3. It decreases

  4. It becomes zero
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

As the spinning top slows down, its angular momentum decreases due to the frictional force.

Multiple choice

What is the angular momentum of a rigid body rotating about a fixed axis with angular velocity (\omega) and moment of inertia (I)?

  1. \(I\omega\)
  2. \(\frac{1}{2}I\omega^2\)
  3. \(2I\omega\)
  4. \(\frac{1}{2}I\omega\)
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

The angular momentum of a rigid body rotating about a fixed axis is given by (I\omega).

Multiple choice

What is the kinetic energy of a rigid body rotating about a fixed axis with angular velocity (\omega) and moment of inertia (I)?

  1. \(\frac{1}{2}I\omega^2\)
  2. \(I\omega\)
  3. \(2I\omega^2\)
  4. \(\frac{1}{2}I\omega\)
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

The kinetic energy of a rigid body rotating about a fixed axis is given by (\frac{1}{2}I\omega^2).

Multiple choice

What is the torque acting on a rigid body rotating about a fixed axis with angular acceleration (\alpha) and moment of inertia (I)?

  1. \(I\alpha\)
  2. \(\frac{1}{2}I\alpha^2\)
  3. \(2I\alpha\)
  4. \(\frac{1}{2}I\alpha\)
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

The torque acting on a rigid body rotating about a fixed axis is given by (I\alpha).

Multiple choice

What is the equation of motion for a rigid body rotating about a fixed axis?

  1. \(I\alpha = \sum\tau\)
  2. \(\frac{1}{2}I\alpha^2 = \sum\tau\)
  3. \(2I\alpha = \sum\tau\)
  4. \(\frac{1}{2}I\alpha = \sum\tau\)
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

The equation of motion for a rigid body rotating about a fixed axis is (I\alpha = \sum\tau).

Multiple choice

What is the angular velocity of a rigid body rotating about a fixed axis with constant angular acceleration (\alpha) and initial angular velocity (\omega_0) after time (t)?

  1. \(\omega_0 + \alpha t\)
  2. \(\omega_0 - \alpha t\)
  3. \(2\omega_0 + \alpha t\)
  4. \(\frac{1}{2}\omega_0 + \alpha t\)
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

The angular velocity of a rigid body rotating about a fixed axis with constant angular acceleration (\alpha) and initial angular velocity (\omega_0) after time (t) is given by (\omega_0 + \alpha t).

Multiple choice

What is the angular displacement of a rigid body rotating about a fixed axis with constant angular acceleration (\alpha) and initial angular velocity (\omega_0) after time (t)?

  1. \(\omega_0 t + \frac{1}{2}\alpha t^2\)
  2. \(\omega_0 t - \frac{1}{2}\alpha t^2\)
  3. \(2\omega_0 t + \alpha t^2\)
  4. \(\frac{1}{2}\omega_0 t + \alpha t^2\)
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

The angular displacement of a rigid body rotating about a fixed axis with constant angular acceleration (\alpha) and initial angular velocity (\omega_0) after time (t) is given by (\omega_0 t + \frac{1}{2}\alpha t^2).

Multiple choice

What is the relationship between the linear velocity (v) of a point on a rigid body rotating about a fixed axis and the angular velocity (\omega) of the body?

  1. \(v = \omega r\)
  2. \(v = \frac{1}{2}\omega r\)
  3. \(v = 2\omega r\)
  4. \(v = \frac{1}{4}\omega r\)
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

The relationship between the linear velocity (v) of a point on a rigid body rotating about a fixed axis and the angular velocity (\omega) of the body is given by (v = \omega r), where (r) is the distance from the point to the axis of rotation.

Multiple choice

What is the relationship between the centripetal acceleration (a_c) of a point on a rigid body rotating about a fixed axis and the angular velocity (\omega) of the body?

  1. \(a_c = \omega^2 r\)
  2. \(a_c = \frac{1}{2}\omega^2 r\)
  3. \(a_c = 2\omega^2 r\)
  4. \(a_c = \frac{1}{4}\omega^2 r\)
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

The relationship between the centripetal acceleration (a_c) of a point on a rigid body rotating about a fixed axis and the angular velocity (\omega) of the body is given by (a_c = \omega^2 r), where (r) is the distance from the point to the axis of rotation.

Multiple choice

What is the center of mass of a uniform rod?

  1. The midpoint of the rod

  2. One-third of the way from one end of the rod to the other

  3. Two-thirds of the way from one end of the rod to the other

  4. The end of the rod
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

The center of mass of a uniform rod is the midpoint of the rod. This is because the mass of the rod is evenly distributed along its length.