Rigid-Body Rotation: Tangential and Normal Accel.

a_{t} = r α a_{n} = r ω^{2} = v^{2} / r

A point at radius r on a rigid body rotating about a fixed axis has tangential acceleration rα (along the path) and normal/centripetal rω² toward the axis. v=rω. Combined a=√(at²+an²).

$ω$ (rad/s): Angular velocity
$α$ (rad/s²): Angular acceleration
$r$ (m): Radius

Step-by-step solved example

r=0.50 m, ω=4 rad/s, α=0. Find an and at.

Point on a rigid body: at = rα tangent, an = rω² inward.

1. Normal
an=0.5×16=8 m/s².
$a_{n} = 8 m/s^{2}$
2. Tangential
at=rα=0.

Answer: an=8 m/s², at=0

10 practice questions

0/10 correct

1.v equals

2.an direction is

3.If ω is constant, at is

4.α = 2 rad/s², r=0.4 m. at=

5.ω must be in

6.Mass moment I about the axis enters ΣM=

7.A point at 2r has an

8.Rolling without slip: v_cm =

9.Total acceleration magnitude is

10.Units of α are