A child plays with a yo-yo with an outer radius of 2.9 cm and a mass of 250 g, equipped with a string wound around the central part of the yo-yo on a circle with an inner radius of 1.3 cm (see diagram below). The moment of inertia of the yo-yo is equal to 1.89×10^-4 kg·m^2. After imparting a clockwise angular velocity ω of 25 rad/s to the yo-yo, the child places the yo-yo against a horizontal surface (coefficient of kinetic friction of 0.17) by pulling vertically on the wound string, as illustrated in the diagram below, using a force  F of 0.80 N. (The child will maintain the magnitude and orientation of the force F during the yo-yo's movement.) Hint: The kinetic friction force is applied forward since the yo-yo has an angular velocity in the clockwise direction and is not moving (it was initially placed on the surface horizontally). Thus, it can be asserted that the yo-yo initially slides on the horizontal surface (it does not roll without sliding!!!). (a) How much time will elapse before the yo-yo rolls without sliding on the horizontal surface? (This moment corresponds to the situation where the tangential velocity of the yo-yo is related to its angular velocity by (vx = r ω ). (b) How many rotations will the yo-yo complete before it rolls without sliding on the horizontal surface?

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The yo-yo
A child plays with a yo-yo with an outer radius of 2.9 cm and a mass of 250 g, equipped with a string wound around the central part of the yo-yo on a circle with an inner radius of 1.3 cm (see diagram below). The moment of inertia of the yo-yo is equal to 1.89×10^-4 kg·m^2.

After imparting a clockwise angular velocity ω of 25 rad/s to the yo-yo, the child places the yo-yo against a horizontal surface (coefficient of kinetic friction of 0.17) by pulling vertically on the wound string, as illustrated in the diagram below, using a force  F of 0.80 N. (The child will maintain the magnitude and orientation of the force F during the yo-yo's movement.)

Hint: The kinetic friction force is applied forward since the yo-yo has an angular velocity in the clockwise direction and is not moving (it was initially placed on the surface horizontally). Thus, it can be asserted that the yo-yo initially slides on the horizontal surface (it does not roll without sliding!!!).

(a) How much time will elapse before the yo-yo rolls without sliding on the horizontal surface? (This moment corresponds to the situation where the tangential velocity of the yo-yo is related to its angular velocity by (vx = r ω ).

(b) How many rotations will the yo-yo complete before it rolls without sliding on the horizontal surface?

 

*Diagram of the yo-yo rotating clockwise above a horizontal surface in the image.*

Outer Radius
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Inner Radius
Transcribed Image Text:Outer Radius 7 ₁ ® ** 2 } Inner Radius
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Transcribed Image Text:18 119 Ixə 8. R
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