NEET Physics: System of Particles and Rotational Motion — Practice Set 4

Q1. A \( 5 \, \text{kg} \) particle moves with velocity \( \mathbf{v} = 4 \, \hat{\mathbf{i}} \, \text{m/s} \) at \( \mathbf{r} = -3 \, \hat{\mathbf{j}} \, \text{m} \). What is the magnitude of its angular momentum about the origin?

Q2. A \( 3 \, \text{kg} \) mass rotates in a circle of radius \( 0.6 \, \text{m} \) with a speed of \( 4 \, \text{m/s} \). What is its angular momentum about the center?

Q3. Why does a ceiling fan continue to rotate after the power is turned off?

Q4. A system consists of two particles: \( 1 \, \text{kg} \) at \( (2, 3) \) and \( 2 \, \text{kg} \) at \( (4, 1) \). What is the y-coordinate of the center of mass?

Q5. What is the direction of torque relative to the force and position vector?

Q6. A particle in a rigid body rotates about a fixed axis at a distance of \( 0.8 \, \text{m} \) with an angular velocity of \( 5 \, \text{rad/s} \). What is its linear speed?

Q7. A solid sphere of mass \( 2 \, \text{kg} \) and radius \( 0.5 \, \text{m} \) has an angular momentum of \( 10 \, \text{kg m}^2/\text{s} \). What is its angular velocity?

Q8. A \( 5 \, \text{kg} \) particle moves with velocity \( \mathbf{v} = 4 \, \hat{\mathbf{i}} \, \text{m/s} \) at \( \mathbf{r} = -2 \, \hat{\mathbf{j}} \, \text{m} \). What is the magnitude of its angular momentum about the origin?

Q9. A force \( \mathbf{F} = 4 \, \hat{\mathbf{i}} - 3 \, \hat{\mathbf{j}} \, \text{N} \) acts at \( \mathbf{r} = 2 \, \hat{\mathbf{i}} + 1 \, \hat{\mathbf{j}} \, \text{m} \). What is the magnitude of the torque about the origin?

Q10. What distinguishes rolling motion from pure rotational motion?

Q11. A \( 3 \, \text{kg} \) particle moves with velocity \( \mathbf{v} = 2 \, \hat{\mathbf{i}} + 3 \, \hat{\mathbf{j}} \, \text{m/s} \) at \( \mathbf{r} = 4 \, \hat{\mathbf{i}} \, \text{m} \). What is the z-component of its angular momentum?

Q12. A uniform rod of mass \( 7 \, \text{kg} \) and length \( 1.5 \, \text{m} \) is pivoted at one end. What is its moment of inertia about the pivot?

Q13. A disk with moment of inertia \( 3 \, \text{kg m}^2 \) rotates at \( 8 \, \text{rad/s} \). A torque of \( 9 \, \text{Nm} \) acts for \( 2 \, \text{s} \). What is its final angular velocity?

Q14. A \( 1 \, \text{kg} \) particle moves with velocity \( \mathbf{v} = -3 \, \hat{\mathbf{i}} + 4 \, \hat{\mathbf{j}} \, \text{m/s} \) at \( \mathbf{r} = 2 \, \hat{\mathbf{i}} \, \text{m} \). What is the z-component of its angular momentum?

Q15. What is the significance of the right-hand rule in determining the direction of a vector product?

Physics — System of Particles and Rotational Motion

Set 4 of 22

22:30

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