Question

In: Physics

String is wrapped around an object of mass M = 0.3 kg and moment of inertia...

String is wrapped around an object of mass M = 0.3 kg and moment of inertia I = 0.01 kgÂ·m2. You pull the string with your hand straight up with some constant force F such that the center of the object does not move up or down, but the object spins faster and faster (see the figure). This is like a yo-yo; nothing but the vertical string touches the object. When your hand is a height y0 = 0.26 m above the floor, the object has an angular speed 0 = 14 radians/s. When your hand has risen to a height y = 0.66 m above the floor, what is the angular speed of the object? Your answer must be numeric and not contain the symbol F.

Expert Solution

Mass of yoyo

Moment of inertia of yoyo

Initial height of hand

Initial angular speed

Final height of hand

Final angular speed is

Work-Energy theorem : work done by all forces is change in kinetic energy.

Kinetic energy of yoyo

Since the position of yoyo did not change,

Work done by hand of person

Change in kinetic energy

Since the yoyo is at rest, acceleration of center of mass of yoyo is zero.

Applying Newtons second law to the yoyo

Final angular velocity

genius_generous answered 2 years ago

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