Rotational Motion: A disk of mass 0.100 kg and radius 0.50 m rotates countercloc
ID: 1486636 • Letter: R
Question
Rotational Motion:
A disk of mass 0.100 kg and radius 0.50 m rotates counterclockwise at a constant angular speed of 10 rad/sec.
1.1) How many revolutions does the disk make in 20 seconds?
1.2) What is the linear speed of the disk at the center? At the edge?
1.4) A teenager pushes the disk such that its angular acceleration is = +0.45 rad/sec^2. What is the angular speed of the disk 10 seconds after the torque is applied? Is it speeding up or slowing down?
1.5) From the data regarding part 1.4, whta is the magnitude and direction of the torque applied to the disk?
thank you
Explanation / Answer
given
m = 0.1 kg
R = 0.5 m
w1 = 10 rad/s
1.1) we know, theta = w*t
= 10*20
= 200 rad
= 200/(2*pi)
= 31.83 rad/s
1.2) v = r*w
= 0.5*31.83
= 15.9 rad/s
1.4) w2 = w1 + alfa*t
= 10 + 0.45*10
= 14.5 rad/s
It is speeding up
1.5) moment of inertia of disk, I = 0.5*m*R^2
= 0.5*0.1*0.5^2
= 0.0125 kg.m^2
Apply, torque, T = I*alfa
= 0.0125*0.45
= 0.005625 N.m
direction : counterclockwise
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