Your roommate is working on his bicycle and has the bike upside down. He spins the 60-cm-diameter wheel, and you notice that a pebble stuck in the tread goes by four times every second. What are the pebble's speed and acceleration?
speed (in m/s) =
acceleration (in m/s^2) =
4 revolutions (2 pi rad) per second
angular velocity w = 2 xpi /4 =1.57 rad/s
speed = w.r = 1.57 x (0.30) =0.47 m/s
acc = w^2 .r = 1.57^2 x 0.30 =0.74 m/s