Question

A rigid object, hinged at one end and initially at rest, is set into rotational motion. Its angular acceleration is given by the equation a = -b + ct where band care constants. Here b = 1.80 rad/s2, and c = 4.80 rad/s3. (a) Write an expression for the angular speed of the object in terms of the constants b, c, and time t. W = (b) Write an expression for the angular position of the object in terms of the constants b, c, and time t. (c) How many revolutions has the object made in the first 8.05 s? rev

Answer 1

Integrate the expression for angular acceleration to find the angular speed. Similarly integrate the expression for angular speed to find the angular position as shown below.

x = -b+ct - -bt t ct + c » c : - btct Jaw = {tbt ct) at tat sa is constant L of integration, at t=0, wzo =) o= -0 tota 3 Cg = 0 So, w = -bt + Ct² = |bt + 0.5 ct²| w = -bt t 0.5c+² => do = -bt to.5cť = (do - Sebt +0.5C+2)dt = 0 = -bť+0.5ct + cz at t=0, 0=0, So C2 = 0 50 - 70.56€ + 0.167cts 2 3 c) 0 = -0.56+0.167Ct3 - put t = 8.055 * 0 - 359 rrad me = 57 rev

***********************************************************************************************
This concludes the answers. If there is any mistake or omission, let me know immediately and I will fix it....