Question

A mass attached to a 66.4 cm long string starts from rest and is rotated 36.6 rev in1 min before reaching a final angular speed. 1. Determine the angular acceleration of the mass, assuming that it is constant. Answer in units of rad/s².2. What is the angular speed of the mass after 1 min? Answer in units of rad/s².

Answer 1

0.128 rad/s², 7.66 rad/s

Step-by-step explanation:

length, l = 66.4 cm

initial angular speed, ωo = 0 rad/s

Let ω be the final angular speed.

Let α be the angular acceleration.

number of revolution, n = 36.6

time, t = 1 min = 60 second

Angle turned, θ = 2πn = 2 x 3.14 x 36.6 = 229.85 rad

Use second equation of motion for angular motion

`\theta =\omega _(0)t+(1)/(2)\alpha t^(2)`

229.85 = 0 + 0.5 x α x 60 x 60

α = 0.128 rad/s²

Use first equation of motion

ω = ωo + αt

ω = 0 + 0.128 x 60

ω = 7.66 rad/s