**Your roommate is working on his bicycle and has the bike upside down. He spins the 62 cm-diameter wheel, and you notice that a pebble stuck in the tread goes by three times every second.
**

**What is the pebble’s speed?
**

**Known Variables:**

**Angular speed**: 3 rev

**Diameter (d) :** 62 cm

Convert angular speed to radians.

3 x 2π = 18.84 rad/s

convert units cm to m.

**radius (r) **= d/2

d=62

d= 62/100

d=.62

r= .62/2

r= .31 m

**Tangential speed, v = rω**

v= (.31) x 18.84

**v= **5.84 m/s

**2) What is the pebble’s acceleration?**

**Equation for radial acceleration:
**

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

(5.84)^{2}/.31 m=

**a**_{c}**=**110.03 m/s^{2}

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