Question

In non-uniform circular motion, the ratio of tangential to radial acceleration is 
\(\textit{(r = radius, \( \alpha \) = angular acceleration, V = linear velocity)}\)

• A. \( \alpha \propto V \)
• B. \( \alpha \propto V^2 \)
• C. \( r^2 \propto \frac{V^2}{\alpha} \)
• D. \( r \alpha^2 \propto \frac{V^2}{\alpha} \)

Hint:

Always remember the relationship between radial and tangential accelerations in non-uniform circular motion.

Answer 1

The Correct Option is C

Step 1: Formula for radial and tangential acceleration.
In circular motion, the radial acceleration is given by \( a_r = \frac{V^2}{r} \) and the tangential acceleration is \( a_t = r \alpha \). To find the ratio of tangential to radial acceleration, we calculate: \[ \frac{a_t}{a_r} = \frac{r \alpha}{\frac{V^2}{r}} = r^2 \propto \frac{V^2}{\alpha} \]
Step 2: Conclusion.
Thus, the correct answer is (C) \( r^2 \propto \frac{V^2}{\alpha} \).