Circular Motion in Vertical Plane

This page discusses uniform circular motion in a vertical plane, such as in vertical loops or circular tracks.

Key points: • Speed remains constant in uniform circular motion • Net torque is zero in circular motion

For an object in vertical circular motion: T - mg = mv²/r (at the bottom) T + mg = mv²/r (at the top)

Where T is tension, m is mass, g is gravitational acceleration, v is velocity, and r is radius.

Example: For a roller coaster car in a vertical loop, the tension in the track is greatest at the bottom of the loop and least at the top.

The page also includes an example of calculating the minimum velocity required for an object to maintain circular motion at the top of a vertical loop.

Highlight: In vertical circular motion, the force of gravity affects the net force at different points in the circle, unlike in horizontal circular motion.

Uniform Circular Motion Basics

This page introduces fundamental concepts of uniform circular motion.

Uniform circular motion involves movement along a circular path at constant speed. While the speed remains constant, the velocity vector continuously changes direction.

Key parameters include:

• Period (T): Time for one complete revolution, measured in seconds • Frequency (f): Number of revolutions per second, measured in hertz (Hz) • Linear velocity (v): Tangential velocity along the circular path • Angular velocity (ω): Rate of angular displacement

Definition: Uniform circular motion is motion in a circular path at constant speed.

Vocabulary: • Period (T): Time for one complete revolution • Frequency (f): Number of revolutions per second

The relationships between these parameters are given by important formulas:

v = 2πr/T = 2πrf ω = 2π/T = 2πf

Highlight: The linear velocity (v) and angular velocity (ω) are related by the formula v = ωr, where r is the radius of the circular path.