## Radius and Speed with Hypothetical Modicfications

**A particle rotates in a circle with centripetal acceleration a= 22 m/s ^{ 2}.**

**a) What is a If the radius is doubled without changing the particle’s speed?**

**a** = v^{2}/r

if radius is doubled,

**a** = v^{2}/2r

or v^{2 }x 1/2

22/2 : By looking at the equation, it should be halved since you are basically multiplying it by 1/2

= 11 m/s

**b) What is a if the speed is doubled without changing the circle’s radius?**

**a** = v^{2}/r

if speed is doubled,

**a** = 2v^{2}/r

or 2 * v^{2 }/ r

22 * 4 ( By looking at the equation, it should be quadrupled since there is a factor of **v ^{2)}**

= 88 m/s

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