Question

A solid disk with r = 1m and M = 1kg falls from unwinding string (as in a primitive yo-yo).

(a) use conservation of energy to find linear speed v once the disk lowers by h = 50cm.

(b) from h = v2/2a find the linear acceleration a

(c) find α, the angular acceleration

Answer 1

(a)

Mass of the disk , m = 1 kg

Radius of the disck , R = 1 m

Moment of Inertia for a solid disc

Height of drop , h = 50 cm = 0.5 m

Law of Conservation of Energy : Initial Energy = Final Energy,

Since the disc is at rest initially at rest, Initial Kinetic Energy = 0

Since the disc is at rest finally at 0 height , Final Potential Energy = 0

but    and   

Substituting

  

  

Final Linear Velocity,

That is the mass or radius of the disc doesnot depend on the final Linear velocity

Substituting   

(b)

From,   

Substituting

(c) From  

Substituting, ====> answer