Question

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A child's spinning top is wound with a string. The top has a moment of inertia...

A child's spinning top is wound with a string. The top has a moment of inertia equal to 12.3 kg m². The string applies a tangential force of 456 N, at a radius of 3.00 cm. The string is wound around the top 8 times, which makes the top rotate through 8 full rotations while the string is being pulled.

a) What is the speed of the top just after the string is pulled?

b) What is its kinetic energy?

Solutions

Expert Solution

Moment of inertia of the top = I = 12.3 kg.m²

Tangential force applied by the string = T = 456 N

Radius at which the tangential force is applied = R = 3 cm = 0.03 m

Angular acceleration of the top =

= 11.122 rad/s²

Number of revolutions made by the top = n = 8

Angle through which the top rotates =

= 50.265 rad

Initial angular speed of the top = ₁ = 0 rad/s

Final angular speed of the top = ₂

₂ = 33.44 rad/s

Final kinetic energy of the top = E

E = 6.88 x 10³ J

a) Speed of the top just after the string is pulled = 33.44 rad/s

b) Kinetic energy of the top = 6.88 x 10³ J

genius_generous answered 1 year ago

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