1. A top is a toy that is made to spin on its pointed end by pulling on a string

Question

1. A top is a toy that is made to spin on its pointed end by pulling on a string wrapped around the body of the top. The string has a length of 52 cm and is wound around the top at a spot where its radius is 1.8 cm. The thickness of the string is negligible. The top is initially at rest. Someone pulls the free end of the string, thereby unwinding it and giving the top an angular acceleration of 14 rad/s2. What is the final angular velocity of the top when the string is completely unwound?
rad/s

(a) What is the angular speed (the magnitude of the angular velocity) of this bacterial motor?
rad/s

(b) How long does it take the motor to make one revolution?
s

3. Suppose you are riding a stationary exercise bicycle, and the electronic meter indicates that the wheel is rotating at 8.1 rad/s. The wheel has a radius of 0.60 m. If you ride the bike for 2150 s, how far would you have gone if the bike could move?
m

Explanation / Answer

1. we know that

S = r*theta

theta = S/r

theta = 52/1.8 = 28.89 rad

Now using equation

wf^2 = wi^2 + 2*alpha*theta

wi = 0

wf = sqrt (2*alpha*theta)

wf = sqrt (2*14*28.89)

wf = 28.44 rad/sec

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