Ayo-yo has a rotational inertia of 1020 g·cm2 and a mass of 83.3 g. its axle radius is 3.71 mm, and its string is 112 cm long. the yo-yo rolls from rest down to the end of the string. (a) what is the magnitude of its linear acceleration? (b) how long does it take to reach the end of the string? as it reaches the end of the string, what are its (c) linear speed, (d) translational kinetic energy, (e) rotational kinetic energy, and (f) angular speed?

Explanation:

It is given that,

Rotational inertia of a yo- yo,

Mass of yo- yo, m = 83.3 g = 0.0833 kg

Radius of axle, r = 3.71 mm = 0.00371 m

Length of the string, l = 112 cm = 1.12 m

(a) The acceleration of the center of mass is given by :

(b) Initially, it is at rest rolls down to the end of the string.

u = 0

Distance, l = 1.12 m

Using second equation of motion as :

(c) Linear speed,

v = 4.6013 m/s

(d) Translational kinetic energy,

(e) Rotational kinetic energy,

Since,

(f) Angular speed,  

Hence, this is the required solution.

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