Free Rotational and Circular Motion MCQs with Answers

• A. Radian
• B. Radian per second
• C. Radian per second2
• D. None

Explanation: Angular acceleration (α) is the rate of change of angular velocity (ω) with respect to time (t):The formula for angular acceleration is…

• A. mass and velocity
• B. momentum and omega
• C. momentum and acceleration
• D. angular momentum and omega

Explanation: The moment of inertia (I) is defined as the ratio of angular momentum (L) to angular velocity (ω), mathematically expressed as I=L/ω .

• A. 2
• B. 1/4
• C. 1/3
• D. 2/3

Explanation: For a hoop rolling without slipping, the total energy is the sum of its translational kinetic energy and rotational kinetic energy.

• A. 24 hrs
• B. 6 hrs
• C. 12 hrs
• D. 3 hrs

Explanation: Reasoning:The duration of a day (the time it takes Earth to rotate once on its axis) is related to its angular momentum.

• A. couple
• B. impulse
• C. torque
• D. angular momentum

Explanation: The moment of momentum is another term for angular momentum. It is the product of the moment of inertia and the angular velocity of an…

• A. 1:4
• B. 4:1
• C. 2:1
• D. √2:1

Explanation: The moment of inertia of a ring is given by I=1/2 mr^2, where m is the mass and r is the radius of the ring.

• A. 1:2
• B. 1:4
• C. 2:1
• D. 8:1

Explanation: This option accurately reflects the calculated ratio.As derived earlier, the moment of inertia of a ring (Ir) is twice that of a disc (Id)…

• A. N
• B. m/s¹
• C. m/s²

Explanation: r.omega^2 represents the centripetal acceleration, where r is the radius of the circular path and Ω is the angular velocity.

• A. Radial velocity and radial acceleration
• B. Tangential velocity and radial acceleration
• C. Tangential velocity and tangential acceleration
• D. Tangential velocity but acceleration having both components

Explanation: As the wheel rotates about an axis passing through the center and perpendicular to the plane, its angular speed increases.

• A. 90°
• B. 180°
• C. 0°
• D. 45°

Explanation: The angle between linear velocity and angular velocity is always 90°. Linear velocity is tangential to the circular path, while angular…

• A. Ir >Id
• B. Ir <Id
• C. Ir −Id
• D. Ir =Id

Explanation: The moment of inertia of a ring is greater than that of a disk of the same mass and radius.

• A. Zero
• B. Minimum
• C. Maximum
• D. Constant

Explanation: Angular momentum is conserved under central forces. In the case of a rotating body under a central force, the angular momentum remains…

• A. Momentum
• B. Force
• C. Inertia
• D. Momentum of inertia

Explanation: The dimensional formula of momentum of inertia is ML^2, where M is the mass and L is the length or radius of rotation.

• A. Remains constant
• B. Becomes zero
• C. Changes continuously
• D. Always increases

Explanation: When a body moves along a circular path, its direction is constantly changing, even if the magnitude of the velocity remains constant.

• A. 80 Nm
• B. 40Nm
• C. 20 Nm
• D. 10 Nm

Explanation: The forces are acted at a distance of 0.2m from the center, the torques is given by 2(100*0.2) = 40 NM.

• A. Momentum
• B. Angular momentum
• C. Torque
• D. Force

Explanation: Angular acceleration is produced by torque according to Newton's second law for rotation, which states that the net torque acting on an…

• A. ΣF=0
• B. ΣF=0, Στ=0
• C. Στ=0
• D. ΣF and Στ≠0

Explanation: For rotational equilibrium, the net force acting on the object must be zero (ΣF=0) and the net torque (Στ) acting on the object must also…

• A. 3%
• B. 5%
• C. 4%
• D. 7%

Explanation: Option (b) is correct because it correctly calculates the maximum error in the moment of inertia considering the errors in mass and radius.

• A. ice skating
• B. gymnastics
• C. diving
• D. all of these

Explanation: The law of conservation of angular momentum is applicable to all the scenarios mentioned: ice skating, gymnastics, and diving.

• A. πMR3/T
• B. πMR2/T
• C. 2πMR2/5T
• D. 4πMR2/5T

Explanation: Here's how to find the angular momentum of the Earth treated as a sphere:1.