Shown below is a solid disc of mass 100 g (M = 100 g), and radius of 10 cm (R= 1

Question

Shown below is a solid disc of mass 100 g (M = 100 g), and radius of 10 cm (R= 10 cm) and moment of inertia about its center of mass equal to Icom= 1/2MR2. The disc is initially rotating at 10 revolutions per second into the page as shown in the top view of the figure. A constant force of 10 N is being applied always tangent to the disc a distance of 2R away from the axis of rotation. Answer the following questions in regards to the conguration. Do not consider any friction or forces due to gravity in this problem. The top view will be the reference for all directions in this problem rotational variable directions will be into the page or out of the page.

Explanation / Answer

here,

mass , m = 0.1 kg

radius , r = 0.1 m

initial angular speed , w = 10 rev/s

force , F = 10 N

(a)

w = 10 rev/s

w = 31.4 rad/s

the magnitude and direction of initial angular velocity is 31.4 ad/sclockwise

(b)

the torque , t = r X F

t = 2 * 0.1 * 10

t = 2 N.m

the torque is 2 N.m out of the page

(c)

the moment of inertia about the rotation axis , I = 0.5 * m * r^2

I = 0.5 * 0.1 * 0.1^2

I = 5 * 10^-4 kg.m^2

the moment of inertia about the rotation axis is 5 * 10^-4 Kg.m/s

(d)

let the angular accelration be alpha

torque = I * alpha

2 = 5 * 10^-4 * aplha

alpha = 4 * 10^3 rad/s^2

the angular accelration is 4 * 10^3 rad/s^2

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