A force of 30 N is applied tangentially to the rim of a solid disk of radius 0.14 m. The disk rotates about an axis through its center and perpendicular to its face with a constant angular acceleration of 130 rad/s2. Determine the mass of the disk.

3.27kg

Explanation:

Inertia can be said to be the resistance of an object to a change in its motion. This includes a change in its direction. An object will stay still or keep moving at the same speed and in a straight line, except it is acted upon by an unbalanced external force.

Given F = 30N

r = 0.14m

a = 130rad/s²

Then, T = Fr

T = 30*0.14

T = 4.2Nm

Also, T = inertia * acceleration

Inertia = 4.2/a

Inertia = 4.2/130

Inertia = 0.032

Also, inertia = mr²/2

0.032 = m * (0.14²)/2

0.032 = m * 0.0098

m = 0.032/0.0098

m = 3.27kg

answer: at 24 february, 2014 the population gets twice of its initial population.

explanation:

since we have given that

the population for alpha city, t years after january 1, 2004 is given as

first we find out the initial population, i.e. t=0,

so, our quadratic equation becomes,

according to question, we have said that if the population has twice its initial population, then it becomes

so, time taken to reach this above mentioned population is given by

now, we know that time can't be negative so, we take t=9.149 years.

hence, at 24 february, 2014 the population gets twice of its initial population.