Circular Motion

Circular Motion Equations

Centripetal Acceleration, Velocity, and Force

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Do Now warm-up prompt

Do Now

At point P, the car hits an area of ice and loses all frictional force on its tires. Which path does the car follow on the ice?

Regents diagram showing a car on a curved track approaching point P, with several possible path choices

June 2001 Regents

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B,

Tangent to the semi-circle

Review - Velocity, Circular Motion

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A. Equations & Vectors

Unicycle circling

Review

Given

Why is an object moving at constant speed in a circle considered to be accelerating?

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Because while its speed is not changing, its direction is.

1. Centripetal Acceleration (ac) - acceleration toward center of curvature

Equation:

ac = V² / r

r - radius,
V - velocity

b) (V) Instantaneous Velocity - tangent to circle, in the direction of the motion

c) Centripetal Force (Fc) - force directed toward the center of the circle

Highlander shot put circling

Ex

Given

A car moving in a circular path with a radius of 2.0 m has a velocity of 8.0 m/s.
Find: the centripetal acceleration of this car.

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ac = V² / r = (8.0 m/s)² / 2.0 m

ac = 64 / 2

ac = 32. m/s²

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Frisbee
Giancoli p. 130) 2, 4

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