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:a. The gear's angular acceleration?

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.b. Through what angle does the motor turn between t = 0 s and the instant at which it reverses direction?

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?

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:b. The tangential acceleration of a tooth on the gear?

CALC A fan blade rotates with angular velocity given by ω_z(t) = g - bt^2, where g = 5.00 rad/s and b = 0.800 rad/s^3. (b) 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?

CALC A fan blade rotates with angular velocity given by ω_z(t) = g - bt^2, where g = 5.00 rad/s and b = 0.800 rad/s^3. (a) Calculate the angular acceleration as a function of time.

CP CALC The angular velocity of a flywheel obeys the equation ω_z(t) = A + Bt2, where t is in seconds and A and B are constants having numerical values 2.75 (for A) and 1.50 (for B). (b) What is the angular acceleration of the wheel at (i) t = 0 and (ii) t = 5.00 s?

CALC The angle θ through which a disk drive turns is given by θ(t) = a + bt - ct^3, where a, b, and c are constants, t is in seconds, and θ is in radians. When t = 0, θ = p/4 rad and the angular velocity is 2.00 rad/s. When t = 1.50 s, the angular acceleration is 1.25 rad/s^2. (c) What are θ and the angular velocity when the angular acceleration is 3.50 rad/s^2?