Answer all parts and show all work and formulas please. Thank you! A massless st

Question

Answer all parts and show all work and formulas please. Thank you!

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 rest to an angular speed of 65 rad/s during a period of 1.9 s. (The toy's spin axis is held fixed and vertical as the string is pulled: the toy rotates, bar it does not translate sideways.) You do NOT need to show your work. Be sure to include correct units and sig.figs.! What is the linear acceleration of the string? How many revolutions does the toy complete during the 1.9 s of acceleration? If the toy's moment of inertia is 1.5 x 10 - 4 kgm2. what is the average net torque that acts on the toy during the 1.9 s? 0n Picture of the toy top above, draw a vector representing the vector direction of tau (torque) acting on the toy's body from the string.

Explanation / Answer

a) alpha = dw/dt = 65 /1.9 = 34.2 rad/s^2

a = alpha r = 34.2*4.2E-2= 1.44 m/s^2

b) theta = w0 t + 1/2 alpha t^2 = 0 + 0.5*34.2*1.9^2= 61.73 rad = 9.82 rev

c)torque = I alpha = 1.5E-3*34.2= 0.0513

d) by righ hand rule torque will be up

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