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. 👁 37
asked by matt
  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
    posted by Christiaan
  2. thank you soooooooo much i really appreciate you taking your time to help

    1. 👍 0
    2. 👎 0
    posted by ed

Respond to this Question

First Name

Your Response

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