Question

The belt-driven pulley and attached disk are rotating with increasing angular velocity. At a certain instant the speed v of the belt is 2.3 m/s, and the total acceleration of point A is 151 m/s2. For this instant determine (a) the magnitude of the angular acceleration of the pulley and disk, (b) the magnitude of the total acceleration of point B, and (c) the magnitude of the acceleration of point C on the belt.

Answer 1

Answer:

a) 1510/$s^{2}$

b) 52.55$m/s^{2}$

c) 52.55$m/s^{2}$

Explanation:

Assuming:

1) Point A is on the periphery of the disk and point B is on periphery of pulley

2) Disk has a radius of 100mm

3) Disk has a radius of 50mm

4) The wheel and the disc experience only rotational motion and there is no slip between he belt and the pulley

a)Since acceleration a of any point on a rotating disc is given as:

                            a=rα

     ⇒                    α=a/r

     ⇒                    α=$\frac{151 m/s^{2} }{100mm}$ = 1510/$s^{2}$

Since pulley and disc are attached to each oter theay have the same angular acceleration.

b) Since point B is on periphery of the pulley, it experiences only rotational motion and no translational motion. Hence:

                               a=rα

      ⇒                      a= 50mm × 1051 $s^{-2}$ = 52.55$m/s^{2}$

c)  Since belt and point B on the pulley experience same motion (pulley is run by the belt), the magnitude of acceleration of point C is same as  point B i.e. 52.55$m/s^{2}$