System of Particles - Rotational Motion Flashcards for NEET — 22 cards

First 8 of 22 System of Particles - Rotational Motion flashcards

Read the question, answer it in your head, then open the answer to check yourself.

1. Card 1 of 22

   What is the formula for the Center of Mass ($R_{cm}$) of a discrete multi-particle system?

   Hint: The position of the CoM is independent of the coordinate system chosen, but its coordinates depend on the origin.

   Show answerHide answer

   Answer

   $R_{cm} = \frac{m_1 r_1 + m_2 r_2 + ... + m_n r_n}{m_1 + m_2 + ... + m_n} = \frac{\sum m_i r_i}{\sum m_i}$

2. Card 2 of 22

   How do you calculate the Center of Mass of a body with a portion removed (Cavity Problems)?

   Hint: Treat the removed portion as a 'negative mass'.

   Show answerHide answer

   Answer

   $x_{cm} = \frac{A_1 x_1 - A_2 x_2}{A_1 - A_2}$ Where $A_1$ is the area/volume of the complete body and $A_2$ is the area/volume of the removed part.

3. Card 3 of 22

   What happens to the trajectory of the Center of Mass of a projectile (like a firecracker) if it explodes in mid-air?

   Hint: Only external forces ($F_{ext}$) can change the acceleration of the CoM.

   Show answerHide answer

   Answer

   The Center of Mass continues to move along the original parabolic trajectory. Internal forces of explosion do not affect the motion of the CoM.

4. Card 4 of 22

   What is the vector relation between linear velocity ($v$) and angular velocity ($\omega$)?

   Hint: Order matters! It is NOT $\vec{r} \times \vec{\omega}$.

   Show answerHide answer

   Answer

   $\vec{v} = \vec{\omega} \times \vec{r}$

5. Card 5 of 22

   Define Torque ($\tau$) and state its vector formula.

   Hint: Maximum torque occurs when the force is applied perpendicular to the position vector ($\theta = 90^\circ$).

   Show answerHide answer

   Answer

   $\vec{\tau} = \vec{r} \times \vec{F}$

6. Card 6 of 22

   Define Angular Momentum ($L$) for a particle and its relation to linear momentum ($p$).

   Hint: For a rigid body rotating about a fixed axis, $L = I\omega$.

   Show answerHide answer

   Answer

   Angular momentum is the moment of linear momentum. $\vec{L} = \vec{r} \times \vec{p}$ Magnitude: $L = mvr \sin(\theta)$

7. Card 7 of 22

   State the relationship between Torque and Angular Momentum (Newton's Second Law for Rotation).

   Hint: Analogous to $\vec{F} = \frac{d\vec{p}}{dt}$.

   Show answerHide answer

   Answer

   The net external torque acting on a system is equal to the rate of change of its angular momentum. $\vec{\tau}_{ext} = \frac{d\vec{L}}{dt}$

8. Card 8 of 22

   State the Law of Conservation of Angular Momentum.

   Hint: Example: An ice skater spinning faster when pulling their arms in (decreasing $I$ increases $\omega$).

   Show answerHide answer

   Answer

   If the net external torque on a system is zero ($\tau_{ext} = 0$), the total angular momentum remains constant. $\vec{L}_{initial} = \vec{L}_{final}$ or $I_1\omega_1 = I_2\omega_2$.