# physics

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?

1. 👍 0
2. 👎 0
3. 👁 63
1. 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

1. 👍 0
2. 👎 0
2. thank you soooooooo much i really appreciate you taking your time to help

1. 👍 0
2. 👎 0
posted by ed

## Similar Questions

1. ### physics

A circle is cut out of a uniform piece of plywood. How does the rotational inertia measured around a point on its outer edge compare with the rotational inertia about its central axis? a. The two rotational inertias are the same.

asked by ChrismB on May 15, 2016
2. ### physics

block 1 has mass m1 = 480 g, block 2 has mass m2 = 540 g, and the pulley is on a frictionless horizontal axle and has radius R = 5.2 cm. When released from rest, block 2 falls 76 cm in 5.2 s (without the cord slipping on the

asked by Ashley on April 2, 2013
3. ### physics

block 1 has mass m1 = 480 g, block 2 has mass m2 = 540 g, and the pulley is on a frictionless horizontal axle and has radius R = 5.2 cm. When released from rest, block 2 falls 76 cm in 5.2 s (without the cord slipping on the

asked by ANS on April 1, 2013
4. ### general physics

An axle of a mass of 10 kg, length 10 cm and radius .1 m is free to rotate about the axis which runs the length of the axle, throuhh it's center. A chain of mass 4kg is fastened to the axle at one end, wound exactly 6 times around

asked by sara on December 9, 2014
5. ### college physics

an atwood machine is constructed by mounting a well-lubricated pulley (not necessarily a ring/disc), whose radius is 6.00cm on an axle and passing a rope over the pulley. Each end of the rope is attached to a different mass of 3.0

asked by kim on June 25, 2013
6. ### Physics

A special pulley has two discs with radii R1 = .8 m and R2 = .35 m. A rope from the R2 disc connects the pulley to a wall and a rope from the R1 disc connects the pulley to a hanging mass. The axle is frictionless. The total mass

asked by Charlie on April 23, 2012
7. ### Physics

A uniform spherical shell of mass M = 19.7 kg and radius R = 1.62 m rotates about a vertical axis on frictionless bearings. A massless cord passes around the equator of the shell, over a pulley of rotational inertia I = 1.02 kg m2

asked by Rhi on June 2, 2012
8. ### AP physics

A uniform spherical shell of mass M and radius R rotates about a vertical axiss on frictionless bearings. A massless cord passes around the equator of the shell, over a pulley of rotational inertia I and radius r, and is attached

asked by Kristen on January 27, 2008
9. ### AP Physics

A uniform spherical shell of mass M and radius R rotates about a vertical axiss on frictionless bearings. A massless cord passes around the equator of the shell, over a pulley of rotational inertia I and radius r, and is attached

asked by Kristen on January 27, 2008
10. ### physics

A uniform spherical shell of mass M = 8.00 kg and radius R = 0.550 m can rotate about a vertical axis on frictionless bearings. A massless cord passes around the equator of the shell, over a pulley of rotational inertia I = 0.130

asked by jr on February 24, 2011

More Similar Questions