physics
posted by matt
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?

Christiaan
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)= 1800 = 180
so the angular velocity after two seconds = 180 rad/s 
ed
thank you soooooooo much i really appreciate you taking your time to help
Respond to this Question
Similar Questions

PHYSICS
An irregularly shaped plastic plate with uniform thickness and density (mass per unit volume) is to be rotated around an axle that is perpendicular to the plate face and through point O. The rotational inertia of the plate about that … 
Physics
A pulley with a rotational interia of 4.4*10^3 kg m^2 about its axle and a radius of 6 cm is acted on by a force applied tangentially at its rim. The force magnitude varies in time as F=0.32t + 0.27t^2 where F is in newtons if t is … 
rotations
A force FT is applied to a cord wrapped around a pulley with moment of inertia I = 0.435 kg·m2 and radius R0 = 33.0 cm. (See the figure.) There is a frictional torque τfr at the axle of 1.10 m·N. Suppose the force FT is given … 
Physics
Figure 1042 shows a uniform disk that can rotate around its center like a merrygoround. The disk has a radius of 2.00 cm and a mass of 20.0 grams and is initially at rest. Starting at time t = 0, two forces are to be applied tangentially … 
physics
A merrygoround in the park has a radius of 1.8 m and a rotational inertia of 900kgm^2. A child pushes the merrygoround with a constant force of 80 N applied at the edges and parallel to the edge. A frictional torque of 12 Nm acts … 
phys
A disk with a rotational inertia of 2.0 kg.m^2 and a radius of 0.40 m rotates on a frictionless fixed axis perpendicular to the disk faces and through its center. A force of 5.0 N is applied tangentially to the rim. The angular acceleration … 
Physics
A solid cylinder is pivoted at its center about a frictionless axle. A force is applied to the outer radius of 1.27 m at an angle of 30 ◦ above the tangential and exerts a force of 5 N. A second force is applied by wrapping rope … 
Physics
A solid cylinder is pivoted at its center about a frictionless axle. A force is applied to the outer radius of 1.27 m at an angle of 30 ◦ above the tangential and exerts a force of 5 N. A second force is applied by wrapping rope … 
physics
A disk with a rotational inertia of 1.4 kg×m2 and a radius of 0.8 m rotates on a frictionless fixed axis perpendicular to the disk faces and through its center. A force of 5.2 N is applied tangentially to the rim. The angular acceleration … 
Physics
A uniform disk with mass 6 kg and radius 1.8 m is pivoted at its center about a horizontal, frictionless axle that is stationary. The disk is initially at rest, and then a constant force 31.5N is applied to the rim of the disk. The …