NEET Physics: System of Particles and Rotational Motion — Practice Set 7

Q1. A \( 3 \, \text{kg} \) object moves with a velocity of \( -5 \, \hat{\mathbf{i}} - 2 \, \hat{\mathbf{j}} \, \text{m/s} \). What is the magnitude of the velocity of its center of mass?

Q2. Why does a larger moment of inertia result in smaller angular acceleration for a given torque?

Q3. A hollow cylinder of mass \( 5 \, \text{kg} \) and radius \( 0.4 \, \text{m} \) rolls without slipping with an angular velocity of \( 8 \, \text{rad/s} \). What is its linear speed?

Q4. A \( 2 \, \text{kg} \) particle moves with velocity \( \mathbf{v} = 4 \, \hat{\mathbf{i}} + 5 \, \hat{\mathbf{j}} \, \text{m/s} \) at \( \mathbf{r} = -3 \, \hat{\mathbf{j}} \, \text{m} \). What is the z-component of its angular momentum?

Q5. What happens to the linear velocity of a particle as its distance from the axis of rotation increases?

Q6. Why is the angular momentum of a symmetric rigid body about a fixed axis often aligned with the axis?

Q7. A thin ring of mass \( 4 \, \text{kg} \) and radius \( 0.3 \, \text{m} \) rotates about its center at \( 8 \, \text{rad/s} \). What is its rotational kinetic energy?

Q8. What is the primary difference between angular momentum and torque?

Q9. What is the physical quantity that measures the rotational inertia of a body?

Q10. In rolling motion of a rigid body without slipping, what is the relationship between linear and angular velocity?

Q11. Vectors \( \mathbf{a} = 5 \, \hat{\mathbf{i}} - 4 \, \hat{\mathbf{j}} \) and \( \mathbf{b} = 3 \, \hat{\mathbf{i}} + 6 \, \hat{\mathbf{j}} \) are given. What is the magnitude of \( \mathbf{a} \times \mathbf{b} \)?

Q12. A particle in a rigid body rotates at a distance of \( 0.25 \, \text{m} \) from a fixed axis with an angular velocity of \( 12 \, \text{rad/s} \). What is its linear speed?

Q13. Why does a body with a larger radius of gyration have greater resistance to rotation?

Q14. A thin ring of mass \( 5 \, \text{kg} \) and radius \( 0.5 \, \text{m} \) has an angular momentum of \( 12.5 \, \text{kg m}^2/\text{s} \). What is its angular velocity?

Q15. A solid cylinder of mass \( 6 \, \text{kg} \) and radius \( 0.5 \, \text{m} \) rolls without slipping with an angular velocity of \( 4 \, \text{rad/s} \). What is its linear speed?

Physics — System of Particles and Rotational Motion

Set 7 of 22

22:30

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A \( 3 \, \text{kg} \) object moves with a velocity of \( -5 \, \hat{\mathbf{i}} - 2 \, \hat{\mathbf{j}} \, \text{m/s} \). What is the magnitude of the velocity of its center of mass?