Comparison of linear and rotational motion — NEET & JEE Questions

Question 1 · difficulty L1 · recall

Which rotational quantity is analogous to mass in linear motion?

• A. Angular velocity
• B. Torque
• C. Moment of inertia
• D. Angular momentum

Question 2 · difficulty L2 · understanding

Which rotational relation is analogous to the linear equation $F=ma$?

• A. $\tau=I\alpha$
• B. $L=I\omega$
• C. $K=\frac12I\omega^2$
• D. $v=r\omega$

Question 3 · difficulty L2 · understanding

Which pair is correctly matched as linear and rotational analogues?

• A. Linear momentum $p$ and angular momentum $L$
• B. Linear momentum $p$ and torque $\tau$
• C. Force $F$ and angular velocity $\omega$
• D. Mass $m$ and angular acceleration $\alpha$

Question 4 · difficulty L2 · understanding

The rotational analogue of linear kinetic energy $\frac12mv^2$ is

• A. $\frac12I\omega^2$
• B. $I\alpha$
• C. $\tau\theta$
• D. $m\omega^2$

Question 5 · difficulty L3 · application

A body of moment of inertia $4\,\text{kg m}^2$ has angular acceleration $3\,\text{rad s}^{-2}$. What torque acts on it?

• A. 1.33 N m
• B. 7 N m
• C. 12 N m
• D. 24 N m

Question 6 · difficulty L3 · application

A rigid body has moment of inertia $2\,\text{kg m}^2$ and angular speed $5\,\text{rad s}^{-1}$. What is its angular momentum about the rotation axis?

• A. 2.5 kg m²/s
• B. 7 kg m²/s
• C. 10 kg m²/s
• D. 25 kg m²/s

Question 7 · difficulty L3 · application

A wheel rotates with angular speed $10\,\text{rad s}^{-1}$. A point on its rim is $0.20\,\text{m}$ from the axis. What is the linear speed of that point?

• A. 0.5 m/s
• B. 2.0 m/s
• C. 10 m/s
• D. 50 m/s

Question 8 · difficulty L3 · application

A constant torque of $6\,\text{N m}$ acts through an angular displacement of $5\,\text{rad}$. How much work is done?

• A. 1.2 J
• B. 11 J
• C. 30 J
• D. 60 J

Question 9 · difficulty L4 · application

A particle moving linearly and a rigid body rotating about a fixed axis each have kinetic energy $K$. If the particle's speed doubles while its mass is unchanged, and the body's angular speed doubles while its moment of inertia is unchanged, how do their kinetic energies change?

• A. Both become $2K$
• B. Both become $4K$
• C. Linear becomes $4K$ but rotational becomes $2K$
• D. Linear becomes $2K$ but rotational becomes $4K$

Question 10 · difficulty L4 · application

A net force on a particle is zero, while a net torque on a rigid body about a fixed axis is non-zero. Which statement best compares their motions?

• A. Neither can accelerate
• B. The particle has zero linear acceleration, while the rigid body can have angular acceleration
• C. The particle must have angular acceleration
• D. The rigid body cannot change angular speed