Question

For uniform circular motion if particle is placed in a pendulum like- setting, why do we take the tensional components and balance them instead of taking components of mg and equating mgcostheta with Tension and mgsintheta = mw^2R

Answer 1

In uniform circular motion, a net force directed towards the center of the circle (centripetal force) is required. Gravity ($mg$) acts vertically downwards and cannot provide this inward force. Tension ($T$) along the string is resolved: its vertical component ($T\cos\theta$) balances $mg$ for horizontal motion ($T\cos\theta = mg$), and its horizontal component ($T\sin\theta$) provides the centripetal force ($T\sin\theta = mv^2/R$). The proposed method is incorrect as $mg\sin\theta$ (a radial component of gravity) acts outward, not inward, and gravity's fixed direction cannot supply the dynamic centripetal force.

Answer 2

Uniform circular motion requires a net force directed towards the center of the circle (centripetal force). Gravity ($mg$) acts vertically downwards and cannot provide this inward force. Tension ($T$) in the string acts along the string. We resolve the tension into components:

1. The vertical component ($T\cos\theta$) balances the force of gravity ($mg$), ensuring the particle moves in a horizontal plane ($T\cos\theta = mg$).
2. The horizontal component ($T\sin\theta$) acts radially inward and provides the necessary centripetal force for circular motion ($T\sin\theta = \frac{mv^2}{R}$). The proposed method of using components of $mg$ is incorrect because:

• A radial component of gravity, $mg\sin\theta$, acts radially outward, not inward.
• Gravity's fixed vertical direction cannot provide the dynamic centripetal force required to change the particle's direction of motion.