Posted by **matt** on Monday, January 28, 2008 at 6:38am.

a pulley with rotational inertia of 1.5 times 10 ^-3 kg times m^2 about its axle and a radius of 15 cm is acted on by a force applied tangentially at its rim. The force magnitude varies in time as F=.5t + .3 t^2, where F is in newtons and t in seconds. The pulley is initiall at rest. At t=2s what is the angualr veloctiy?

- physics -
**Christiaan**, Monday, January 28, 2008 at 7:23am
First we calculate the torque.

t=rxF=r.F.sin(b) where is the angle between r and F (which in this case equals 90°).

So in this case t= r.F = 0,15m.F = 0.075t + 0.045t²

We also know that I = 1.5 . 10^-3 kg.m²

and so we can calculate the angular acceleration (a) with the formula:

t = I.a

=> a = t/I = 50t + 30t²

Now, we need to find the angular velocity after 2 seconds. Since a=dw/dt (with w, the angular velocity), we can find the angular by taking the definite integral of a for t from 0 to 2

=> w = integral of 50t+30t² from 0 to 2=

(25.(2)²+10(2)^3)-(25.(0)²+10(0)^3)= 180-0 = 180

so the angular velocity after two seconds = 180 rad/s

- physics -
**ed**, Monday, January 28, 2008 at 7:24am
thank you soooooooo much i really appreciate you taking your time to help

## Answer This Question

## Related Questions

- Physics - A pulley with a rotational interia of 4.4*10^-3 kg m^2 about its axle ...
- physics - A disk with a rotational inertia of 1.4 kg×m2 and a radius of 0.8 m ...
- rotations - A force FT is applied to a cord wrapped around a pulley with moment ...
- phys - A disk with a rotational inertia of 2.0 kg.m^2 and a radius of 0.40 m ...
- PHYSICS - An irregularly shaped plastic plate with uniform thickness and density...
- physics - A merry-go-round in the park has a radius of 1.8 m and a rotational ...
- Physics... rotation - A constant force of 40 N is applied tangentially to the ...
- Physics - A merry-go-round in the park has a radius of 1.8 m and a rotational ...
- AP physics - A uniform spherical shell of mass M and radius R rotates about a ...
- AP Physics - A uniform spherical shell of mass M and radius R rotates about a ...

More Related Questions