6.1 Uniform circular Motion

Chapter Overview

• Circular Motion & Gravity: Objects moving in circles have centripetal acceleration and require net inward force.

Apparent Forces

• Riders feel an apparent force against the wall in circular motion, leading to the sensation of weight.

Gravity in Orbit

• Satellites, like space stations, are affected by gravity, which keeps them in orbit.

Uniform Circular Motion

• Acceleration in circular motion directs toward the center; constant speed does not mean constant velocity.

• Centripetal acceleration formula: $a = \frac{v^2}{r}$.

Period, Frequency, and Speed

• Period (T): Time for one full revolution. Frequency (f): Number of revolutions per second. Formula: $f = \frac{1}{T}$.

• Velocity related to period and radius: $v = \frac{2 \pi r}{T}$.

Acceleration in Circular Motion

• Centripetal acceleration also represented as: $a = \frac{v^2}{r} = (2 \pi f)^2 r = \frac{4 \pi^2 r}{T^2}$.

Example Problems

• Table Saw Example: Analyze tooth speed/acceleration; apply circular motion equations.

• Carnival Ride Example: Calculate period/speed of ride under maximum acceleration conditions.

Ranking Periods of Motion

• Longer radius => longer period; higher speed => shorter period. Rank motion periods by radius and speed considerations.