Question

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 these 15 seconds? e. Calculate the total distance traveled by a point on the rim during the 15 seconds f. Calculate the tangential acceleration of a point on the rim at the time t 15 s Calculate the radial acceleration of a point on the rim at the time t 15 s

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Answer 1

The direction of the angular velocity = into the page or - k [using right hand rule, the disk is rotating in clockwise direction) since the angular speed of the disk decreases as time increases Hence the angular acceleration must be in counter clockwise direction so its direction so its direction Rightarrow k (out of the page) using w_f = w_i + alpha to find alpha alpha = w_f - w_i/t t = 15r w_f = 13 rad/s, w_i = 34 rad/s alpha = 13 - 34/15 = 1.4 rad/s^2 so the magnitude of the angular acceleration alpha = 1.4 rad/s^2 using Delta Theta = w_i t + 1/2 alpha t^2 to get the Delta Theta angular displacement of the disk Delta Theta = 34 * 15 + (- i.4/2) times 15^2 = 352.5 radians