here,
diameter , d = 9 m
radius , r = 4.5 m
theta = 2.9 t^2 - 0.65 *t^3
(a)
angular speed w = dθ/dt = 5.8*t - 1.95 *t^2
dw/dt = 5.8 - 3.9 t
dw/dt = 0 for max w
so max w occurs at t = 5.8/3.9 s
t = 1.49 s
so w max = 5.8 * 1.49 - 1.95 * (1.49)^2
wmax = 4.31 rad/s
(b)
tangential speed v = r*w
so v = 0.5 * 4.31
v = 2.16 m/s
(c)
w is positive until 5.8 t = 1.95 *t^2
so t = 5.8/1.95
t = 2.97 s (or t = 0 invalid)
After t = 2.97s
, w is negative (starts reversing direction of rotation)
Driving force would actually have to be removed some time before t = 2.97 s because the roller can't stop instantaneously, but insufficient info to calculate this.
(d)
Up to t = 2.97s,
theta = 2.9 * 2.97^2 - 0.65 * 2.97^3
theta = 8.63 rad = 1.37 rotations
In a manufacturing process, a large, cylindrical roller is used to flatten material fed beneath it....
In a manufacturing process, a large, cylindrical roller is used to flatten material fed beneath it. The diameter of the roller is 4.00 m, and, while being driven into rotation around a fixed axis, its angular position is expressed as θ = 2.30t2 − 0.850t3 where θ is in radians and t is in seconds. (a) Find the maximum angular speed of the roller. rad/s (b) What is the maximum tangential speed of a point on the rim of the...
A disk-shaped machine part has a diameter of 37.0 cm. Its angular position is given by 0 = -1.37€ + 1.80t2, where t is in seconds and O is in radians. (a) What is the maximum angular speed of the part during this time interval? (Assume the time interval is from t= 0 to when the part reverses its direction.) rad/s (b) What is the maximum tangential speed of a point halfway to the rim of the part during this...
please help A uniform disk of radius 0.65 m rotates clockwise about its central axis and accelerates with constant angular acceleration. At time 1-0 it is rotating at 34 rad/s, at timeに15 s later, its angular speed is 13 rad/s. (Recall 2π rad-1 rev). a. What is the direction of the angular velocity? b. What is the direction of the angular acceleration? c. Calculate the magnitude of the angular acceleration d. Through how many radians has the disk turned in...
Please solve for Tf and how fast the neuron star rotate in rotations per seconds. Formation of a Neutron Star A star rotates with a period of 29 days about an axis through its center. The period is the time interval required for a point on the star's equator to make one complete revolution around the axis of rotation. After the star undergoes a supernova explosion, the stellar core, which had a radlus of 1.5 x 104 km, collapses into...
5:16 lLTE ) Done 1 of 5 Assessment #1 (Kinematics of a Particle) Rectilinear Motion (Straight linc Motion 3. The position of a point during the interval of time from r otor 6 is given by ** * m. (a) What is the maximum velocity during this interval of time, and at what time does it occur? (b) What is the acceleration when the velocity is a maximum? (20 m/s, 0 m/s 3. A test projectile is fired horizontally into...