A wheel 2.12 m in diameter lies in a vertical plane and rotates about its central axis with a constant angular acceleration of 3.52 rad/s. The wheel starts at rest at t = 0, and the radius vector of a certain point P on the rim makes an angle of 57.30 with the horizontal at this time. At t = 2.00 s, find the following. (a) the angular speed of the wheel (b) the tangential speed of the point P (c) the total acceleration of the point P (d) the angular position of the point P Part 1 of 6 - Conceptualize Visualize a large carnival roulette wheel. It spins at several radians per second. A point on the rim will have a rather large centripetal acceleration and a smaller tangential acceleration. Part 2 of 6 - Categorize Parts (a) and (d) are about the kinematics of rotation, describing rotation with constant @. In parts (b) and (c), we relate rotation at one instant to the linear motion of a point on the object, through angular position measured in radians. Part 3 of 6 - Analyze We are given a = 3.52 rad/s , w; = 0, 8, = 57.30 = 1 rad, and t = 2 s. (a) We choose the equation wy = w; + at = 0 + at, which gives the following. wf = 3.52 4 3.52 rad/s2) 2 P z s = 7.04 8 7.04 r Part 4 of 6 - Analyze (b) We are also given r = 1.06 m. The tangential speed of a point P on the rim is V = rw = 7.04 1X Your response differs from the correct answer by more than 100%. m)( 7.04 rad/s) = 131 1x Your response differs significantly from the correct answer. Rework your solution from the beginning and check each step carefully, m/s.Tutorial Exercise A disk 8.11 cm in radius rotates at a constant rate of 1 255 rev/min about its central axis. (a) Determine its angular speed in radians per second. (b) Determine the tangential speed at a point 3.11 cm from its center. (c) Determine the radial acceleration of a point on the rim. (d) Determine the total distance a point on the rim moves in 1.95 s. Part 1 of 5 - Conceptualize If this is a sanding disk driven by a workshop electric drill, for example, the acceleration of a point on the circumference is many times g. Part 2 of 5 - Categorize We will use radian measure to relate rotation of the whole object to linear motion of a point on the object. Part 3 of 5 - Analyze (a) For angular speed in radians per second, we have w = 2nf = (21 rad/rev 1255 1260 rev/min 60 s/ min = 131.42 131 rad/s (b) And for the tangential speed at a point 3.11 cm from the center, v = wr 131.42 131 rad /5 3.11 / 3.11 x 10-2 m) 4.09 4.09 m/s. Part 4 of 5 - Analyze (c) We use the following to find the magnitude of the radial acceleration of a point on the rim. 3 c = war 131.42 rad/s) 4.09 Your response differs from the correct answer by more than 10%. Double check your calculations. * 10-2 m) 537.13 X Your response differs significantly from the correct answer. Rework your solution from the beginning and check each step carefully. x 103 m/=2