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S5.4 Constant acceleration equations

[A] Rotation with constant acceleration

Consider the motion of a body rotating about a fixed axis, with constant acceleration.

Worked example

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Worked example

A record player turntable (radius 0.152m) starts from rest and turns with constant angular acceleration to reach a final angular speed of 33.3 rev/min after 3s. Find the components of the linear acceleration at the rim, 2s after starting.

Solution

The angular acceleration is

\[ \alpha=\frac{\Delta \omega}{\Delta T}=\xmlInlineElement[\xmlAttr{}{target}{slides}]{http://www.ph.ed.ac.uk/aardvark/NS/aardvark-latex}{aardvark:reveal}{\frac{33.3\times 2\pi/60 }{3}=1.16\;} rad\; s^{-2} \]

From KP 6.11, the angular velocity after 2s is

ω(t=2s)=0+1.16×2=2.32 rad s-1

and thus

\[ a_r=\frac{v^2}{r}=r\omega^2=0.818 \; m\;s^{-2} \]

at=rα=0.152×1.16=0.176 m s-2

 

Learning Resources

Textbook: HRW Chapter 10.4
Course Questions:
Self-Test Questions: