Need a bit of help -- Pulley accelerated by a force....

[CentrifugalKing]

Homework Statement

A pulley, with a rotational inertia of 1.5✕ 10-3kg·m2 about its axle and a radius of 10 cm, is acted on by a force applied tangentially at its rim. The force magnitude varies in time as F = 0.50t + 0.30t2, where F is in Newtons and t in seconds. The pulley is initially at rest.

Find angular velocity at t=7s


(a) Calculate the torque required to accelerate the Earth in 7 days from rest to its present angular speed about its axis.

Homework Equations

The Attempt at a Solution

Okay, for the first one, I integrated the Force and got

(0.5t^2)/2 + (0.3t^3)/3 = I (alpha) and entered the equation.

For the second, I'm found the Moment of Inertia of Earth to be 9.74e37 and tried to find angular velocity by this

(2 (pi))/604800

The 604800 is the amount of seconds in 7 days on Earth.

Please help and thank you in advance.

 

[J Hann]

Don't you need to calculate the current angular velocity of the Earth (1 rev) / day?
Then from that you can calculate the required angular acceleration.

 

[CentrifugalKing]

@J Hann

I thought I did with the "2pi/604800" part. So that's velocity? How would I get acceleration?

 

[J Hann]

@J Hann

I thought I did with the "2pi/604800" part. So that's velocity? How would I get acceleration?

The Earth makes 1 (2 pi) revolution in 60 * 60 * 24 = 86400 sec.
That is the present angular speed.
Now you need to find the angular acceleration to reach that speed in 7 days!

 

[haruspex]

I thought I did with the "2pi/604800" part. So that's velocity?

You took an angle, 2pi radians, and divided it by 7 days. That would give you the angular velocity required to rotate once in 7 days.