CALC? The angle ? through which a disk drive turns is given by ?(t) = a + bt - ct3, where a, b, and c are constants, t is in seconds, and ? is in radians. When t = 0, ? = ?/4 rad and the angular velocity is 2.00 rad/s. When t = 1.50 s, the angular acceleration is 1.25 rad/s2. (a) Find a, b, and c, including their units. (b) What is the angular acceleration when ? = ?/4 rad? (c) What are and the angular velocity when the angular acceleration is 3.50 rad/s2?
Solution 7E Step 1 of 4: d d z zt) = dt, zt) = dt To calculate a, b and c use the values of Step 2 of 4: a)(t) = a + bt ct 3 3 zt) = d = d( a + bt ct ) dt dt 2 zt) = b 3ct At t = 0, = a = rad and = b = 2 rad/s 4 z 2 dz = d(b3ct ) dt dt zt) = 6ct. At t = 1.5 s, =z 6c(1.5 s) 2 3 = 1.25 rad/s and c = 0.139 rad/s