SUMMARY
The centripetal acceleration of a disc after spinning up can be calculated using the formula \( a_c = -\omega^2 r \) or \( a_c = -\frac{v^2}{r} \). In this discussion, the disc accelerates with an angular acceleration of \( \alpha = 506 \, \text{rad/s}^2 \) for 1.66 seconds, with a radius of 3.9 cm. To find the angular velocity (\( \omega \)) after 1.66 seconds, one must integrate the angular acceleration over time, resulting in \( \omega = \alpha \cdot t \). The final centripetal acceleration can then be computed using the determined angular velocity.
PREREQUISITES
- Understanding of angular acceleration and its implications
- Familiarity with centripetal acceleration formulas
- Basic knowledge of calculus for integrating angular acceleration
- Concept of rotational motion and its parameters
NEXT STEPS
- Calculate angular velocity using \( \omega = \alpha \cdot t \)
- Explore the relationship between linear and angular velocity
- Learn about the effects of varying angular acceleration on centripetal force
- Study real-world applications of centripetal acceleration in mechanical systems
USEFUL FOR
Physics students, mechanical engineers, and anyone studying rotational dynamics and centripetal forces will benefit from this discussion.