A painted tooth on a spinning gear has angular position θ = (6.0 rad/s⁴)t⁴. What is the tooth's angular acceleration at the end of 10 revolutions?

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 three times every second. What are the pebble's speed and acceleration?

A 5.0-m-diameter merry-go-round is initially turning with a 4.0 s period. It slows down and stops in 20 s. How many revolutions does the merry-go-round make as it stops?

Starting from rest, a DVD steadily accelerates to 500 rpm in 1.0 s, rotates at this angular speed for 3.0 s, then steadily decelerates to a halt in 2.0 s. How many revolutions does it make?

The angular velocity of a process control motor is ω = ( 20 ─ ½ t² ) rad/s, where t is in seconds. Through what angle does the motor turn between t = 0 s and the instant at which it reverses direction?

A 6.0-cm-diameter gear rotates with angular velocity ω = ( 20 ─ ½ t² ) rad/s where t is in seconds. At t = 4.0 s, what are: The tangential acceleration of a tooth on the gear?

A 6.0-cm-diameter gear rotates with angular velocity ω = ( 20 ─ ½ t² ) rad/s where t is in seconds. At t = 4.0 s, what are: The gear's angular acceleration?

A fan blade rotates with angular velocity given by ω_z(t) = g - bt², where g = 5.00 rad/s and b = 0.800 rad/s³. Calculate the instantaneous angular acceleration α_z at t = 3.00 s and the average angular acceleration α_av-z for the time interval t = 0 to t = 3.00 s. How do these two quantities compare? If they are different, why?

A fan blade rotates with angular velocity given by ω_z(t) = g - bt², where g = 5.00 rad/s and b = 0.800 rad/s³. Calculate the angular acceleration as a function of time.