Physics

A wheel mounted on a stationary axle starts at rest and is given the following angular acceleration: 9-12t where t is the time after the wheel begins to rotate. Find the number of revolutions that the wheel turns before it stops ( and begins to turn in the opposite direction).

  1. 👍 1
  2. 👎 1
  3. 👁 552
  1. dv/dt = 9 - 12 t and v(0)= 0

    v = 9 t - 6 t^2 + constant
    when t = 0, v = 0 so constant = 0
    v is radians/sec

    v = 9 t - 6 t^2
    at v = 0
    0 = t(9-6t)
    so v = 0 at t = 0 as we knew
    and
    v = 0 at t=9/6 = 3/2 = 1.5
    so how far did it go?
    x is radians
    x = (9/2) t^2 - (6/3)t^3 + 0
    x = (9/2)(9/4) - (6/3)(9/4)(3/2)
    = 81/8 - 54/12
    = (243 - 108)/24
    =135/24 radians
    check my arithmetic
    divide by 2 pi to get revolutions

    1. 👍 1
    2. 👎 1

Respond to this Question

First Name

Your Response

Similar Questions

  1. physics

    A wheel starts from rest and rotates with constant angular acceleration and reaches an angular speed of 12.0 rad/s in 3.00 s. Find the angle (in radians) throuh which it rotates in this time.

    asked by Godwin on September 3, 2015
  2. physics

    a wheel starts from rest on application of torque which gives it an angular acceleration @=2t^2-t^2 for first two seconds after which @= 0 then find angular velocity of wheel after 4 seconds.

    asked by Priya on July 29, 2017
  3. phys

    A wheel starts from rest and has an angular acceleration of 4.0 rad/s^(2). When it has made 10 rev its angular velocity is:

    asked by jay on April 27, 2014
  4. physics

    A flywheel with a diameter of 1 m is initially at rest. Its angular acceleration versus time is graphed in the figure. (a) What is the angular separation between the initial position of a fixed point on the rim of the flywheel and

    asked by Help..Help !!!! on March 21, 2011
  5. physics

    A small rubber wheel is used to drive a large pottery wheel, and they are mounted so that their circular edges touch. The small wheel has a radius of 1.7 cm and accelerates at the rate of 6.9 rad/s^2, and it is in contact with the

    asked by rob on October 18, 2010
  1. physics

    A flywheel with a diameter of 1 m is initially at rest. Its angular acceleration versus time is graphed in the figure. (a) What is the angular separation between the initial position of a fixed point on the rim of the flywheel and

    asked by HARD!!!! on March 20, 2011
  2. physics

    A 4.00-m length of light nylon cord is wound around a uniform cylindrical spool of radius 0.500 m and mass 1.00 kg. The spool is mounted on a frictionless axle and is initially at rest. The cord is pulled from the spool with a

    asked by Mike on March 19, 2012
  3. physics

    A flywheel with a diameter of 1 m is initially at rest. Its angular acceleration versus time is graphed in the figure. (a) What is the angular separation between the initial position of a fixed point on the rim of the flywheel and

    asked by Anonymous on March 20, 2011
  4. Physics

    A device consists of eight balls each of mass 0.4 kg attached to the ends of low-mass spokes of length 1.8 m, so the radius of rotation of the balls is 0.9 m. The device is mounted in the vertical plane. The axle is held up by

    asked by Emily on April 14, 2013
  5. Physics

    A wheel with rotational inertia I is mounted on a fixed, fricitonless axle. The angular speed w of the wheel is inccreased from zero to w_f in a time interval T. 1: What is the average net torque on the wheel during the time

    asked by Tammy on March 25, 2007
  6. PHYSICS

    AN AUTOMOBILE TIRE HAS A RADIUS OF 0.330M AND ITS CENTER MOVES FORWARD WITH A LINEAR SPEED OF V= 15.0M/S. a) DETERMINE THE ANGULAR SPEED OF THE WHEEL. B) RELATIVE TO THE AXLE, WHAT IS THE TANGENTIAL SPEED OF A POINT LOCATED 0.175M

    asked by kassy on November 8, 2016

You can view more similar questions or ask a new question.