A string is wound around a uniform disc of radius 0.68 m and mass 3.7 kg. The disc is released from rest with the string vertical and its top end tied to a fixed support. calculate the speed of the center of mass when, after starting from rest, the center of mass has fallen 1.2 m. The acceleration of gravity is 9.8 m/s 2 . Answer in units of m/s.

3.962

Explanation:

mass = 1.2

gravity g = 9.81

velocity = ?

mgh = 1/2mv² + 1/2(1/2)mv²

= 9.81 x 1.2  = 3/4v²

11.772 x 4 = 3/4v²

47.088 = 3v²

divide through both sides by 3

15.696 = v²

take the square root of both sides

√15.696 = √v²

= 3.6962 = v

the speed is therefore 3.692

pythagoras' theorem

square root (-5^2+9^2)

square root (25+81)

square root (106)

angle is tan^-1(9/5)

neg x, pos y