What is the Speed and Acceleration?

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= v²/r

(5.84)²/.31 m=

a_c=110.03 m/s²