A massless string is wound around the outer edge of a toy top (radius 4.2 cm). W

Question

A massless string is wound around the outer edge of a toy top (radius 4.2 cm). When the string is pulled with a constant acceleration, the top "spins up" from the rest to an angular speed of 65 rad/s during a period of 1.9s. (The toy's spin axis is held fixed and vertical as the string is pulled; the toy rotates, but it does not translate sideways.)

a. What is the linear acceleration of the string?

b. How many revolutions does the toy complete during the 1.9s of acceleration?

c. If the toy's moment of inertia is 1.5x10^-4 kg*m^2, what is the average net torque that acts on the toy during the 1.9s?

d. On the picture of the toy top above, draw a vector representing the vector direction of torque acting on the toy's body from the string.

Explanation / Answer

a) a = 65/1.9 = 34.21052631579 rad/s^2

thus acc = (4.2/100)*34.21052631579 = 1.43684210526318 m/sec^2

b) d = 0.5*a*t^2 = .5* 34.21052631579*1.9*1.9 =61.75 rad

thus revolutions = 61.75/2pi =9.832802547771

c)T = 34.21052631579*1.5/10000 = 0.0051315789473685 N/m

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