NEET System of Particles and Rotational Motion — Set 14

Question 1

A torque of $ 20 \, \text{Nm} $ is applied to a wheel with moment of inertia $ 4 \, \text{kg m}^2 $. What is its angular acceleration?

Accepted Answer

$ \tau = I \alpha $. $ \tau = 20 \, \text{Nm} $, $ I = 4 \, \text{kg m}^2 $. $ \alpha = \frac{\tau}{I} = \frac{20}{4} = 5 \, \text{rad/s}^2 $.

Question 2

Two particles of masses $ 6 \, \text{kg} $ and $ 4 \, \text{kg} $ are at $ (2, 3) $ and $ (8, 7) $ respectively. What is the distance of their center of mass from the origin?

Accepted Answer

$ X = \frac{(6 \times 2) + (4 \times 8)}{6 + 4} = \frac{12 + 32}{10} = 4.4 $. $ Y = \frac{(6 \times 3) + (4 \times 7)}{6 + 4} = \frac{18 + 28}{10} = 4.6 $. Distance = $ \sqrt{(4.4)^2 + (4.6)^2} = \sqrt{19.36 + 21.16} = \sqrt{40.52} \approx 6.36 \, \text{m} $.

Question 3

Why does a body with zero net torque maintain its rotational state?

Accepted Answer

Zero net torque ($ \mathbf{\tau} = 0 $) means no change in angular momentum ($ \frac{d\mathbf{L}}{dt} = 0 $), so the rotational state (angular velocity) remains constant.

NEET Physics: System of Particles and Rotational Motion — Practice Set 14

Q1. A torque of \( 20 \, \text{Nm} \) is applied to a wheel with moment of inertia \( 4 \, \text{kg m}^2 \). What is its angular acceleration?

Q2. Two particles of masses \( 6 \, \text{kg} \) and \( 4 \, \text{kg} \) are at \( (2, 3) \) and \( (8, 7) \) respectively. What is the distance of their center of mass from the origin?

Q3. Why does a body with zero net torque maintain its rotational state?

Q4. A force \( \mathbf{F} = -2 \, \hat{\mathbf{i}} + 3 \, \hat{\mathbf{j}} \, \text{N} \) acts at \( \mathbf{r} = 1 \, \hat{\mathbf{i}} + 2 \, \hat{\mathbf{j}} \, \text{m} \). What is the torque about the origin?

Q5. A force \( \mathbf{F} = 5 \, \hat{\mathbf{i}} + 4 \, \hat{\mathbf{j}} \, \text{N} \) acts at \( \mathbf{r} = -3 \, \hat{\mathbf{i}} - 2 \, \hat{\mathbf{j}} \, \text{m} \). What is the magnitude of the torque about the origin?

Q6. A \( 3 \, \text{kg} \) mass rotates in a circle of radius \( 0.7 \, \text{m} \) with a speed of \( 4.2 \, \text{m/s} \). What is its angular momentum about the center?

Q7. A solid cylinder of mass \( 4 \, \text{kg} \) and radius \( 0.2 \, \text{m} \) rolls without slipping with a linear speed of \( 2 \, \text{m/s} \). What is its angular velocity?

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

Q9. A \( 2 \, \text{kg} \) mass rotates in a circle of radius \( 0.5 \, \text{m} \) with a speed of \( 8 \, \text{m/s} \). What is its angular momentum about the center?

Q10. A \( 2 \, \text{kg} \) particle moves with velocity \( \mathbf{v} = -5 \, \hat{\mathbf{i}} - 3 \, \hat{\mathbf{j}} \, \text{m/s} \) at \( \mathbf{r} = 4 \, \hat{\mathbf{i}} \, \text{m} \). What is the z-component of its angular momentum?