The figure shows a child\'s top, of outer radius R = 3.0cm, which is made to spi

Question

The figure shows a child's top, of outer radius R = 3.0cm, which is made to spin about its vertical axis by pulling a string. The end of this string, which is wound around a stem of radius r = 0.50cm, is pulled with a constant linear acceleration a = 0.25m/s^2. Initially the top is at rest, and after time t = 2.0s, the full length L = 0.50m of the string is unwound. What is the angular acceleration of the top while the string is being pulled? How many revolutions does the top make while it is being unwound? The top has small beads embedded in its outer surface of radius R. Calculate the magnitudes of the tangential and radial components of the acceleration of these beads at t = 2.0s.

Explanation / Answer

a. angular acceleration= linear acceleration/radius= 0.25 /0.5 x10^-2= 50 rad/s^2

b.0.5 = 2xpi x 0.5 x 10^-2 x n

so, n= 15.91 revolutions

c.tangential acceleration= 50 x 3 x10^-2=1.5 rad/s^2

angular velocity at 2s= 50 x 2= 100 rad/s

linear velocity = angular velocity x radius= 100 x 3x10^-2=3m/s

radial component of acceleration = 3^2/2g= 0.46 m/s^2

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