A uniform disk with a mass of 2.00 kg and a radius of 80.0 cm is free to spin li
ID: 1485649 • Letter: A
Question
A uniform disk with a mass of 2.00 kg and a radius of 80.0 cm is free to spin like a wheel on a frictionless axle, but is initially at rest. A force of constant magnitude is suddenly applied tangentially to the rim, so that the disk rotates clockwise, and its rotation rate rises from zero to 250 rpm during the course of the first 15 complete rotations. The moment of inertia of a uniform disk spinning like a wheel is given by.
(a) Calculate the magnitude of the angular acceleration of the wheel during this time. (Answer: 3.64 rad/s2)
(b) Calculate the magnitude of the force applied to the rim. (Answer: 2.912 N)
Explanation / Answer
Moment of inertia , I =mr^2/2 = 2*(0.8)^2/2 = 0.64 kg-m^2
a)
intial velocity = 0
final angular velocity = 250 rpm = 250*2pi/60 = 26.166 rad/s
angular displacement = 15 rev = 15*2pi = 30*pi = 94.2 rad
from the relation
w^2 -wo^2 = 2as
26.166^2 - 0 = 2*a *94.2
anguar acceleration ,a = 3.634 rad/s^2
b)
rF = I a
0.8*F = 0.64*3.634
Force , F = 2.91 N
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