Irodov – Problems in General Physics

Fig. 1.5.

1.44. A wheel rotates around a stationary axis so that the rotation

angle p varies with time as cp = ate, where a = 0.20 rad/s 2. Find the

total acceleration w of the point A at the rim at the moment t = 2.5 s

if the linear velocity of the point A at this moment v = 0.65 m/s.

1.45. A shell acquires the initial velocity v = 320 m/s, having

made n = 2.0 turns inside the barrel whose length is equal to 1 =

= 2.0 m. Assuming that the shell moves

inside the barrel with a uniform accelera- (^) A
tion, find the angular velocity of its axial
rotation at the moment when the shell
escapes the barrel.
1.46. A solid body rotates about a station-
ary axis according to the law IT = at -

• bt 3 , where a = 6.0 rad/s and b = 2.0
  rad/s 3. Find:
  (a) the mean values of the angular velo-
  city and angular acceleration averaged over
  the time interval between t = 0 and the
  complete stop;
  (b) the angular acceleration at the moment when the body stops.
  1.47. A solid body starts rotating about a stationary axis with an
  angular acceleration 13 = at, where a = 2.0.10-2 rad/s 3. How soon
  after the beginning of rotation will the total acceleration vector of
  an arbitrary point of the body form an angle a = 60° with its velo-
  city vector?
  1.48. A solid body rotates with deceleration about a stationary
  axis with an angular deceleration f3 oc -troT, where co is its angular
  velocity. Find the mean angular velocity of the body averaged over
  the whole time of rotation if at the initial moment of time its angular
  velocity was equal to co,.
  1.49. A solid body rotates about a stationary axis so that its angu-
  lar velocity depends on the rotation angle cp as co = coo — acp, where
  co o and a are positive constants. At the moment t = 0 the angle
  = 0. Find the time dependence of
  (a) the rotation angle;
  (b) the angular velocity.
  1.50. A solid body starts rotating about a stationary axis with an
  angular acceleration it = 1 0 cos p, where Po is a constant vector and cp
  is an angle of rotation from the initial position. Find the angular
  velocity of the body as a function of the angle cp. Draw the plot of
  this dependence.
  1.51. A rotating disc (Fig. 1.6) moves in the positive direction of
  the x axis. Find the equation y (x) describing the position of the
  instantaneous axis of rotation, if at the initial moment the axis C
  of the disc was located at the point 0 after which it moved
  (a) with a constant velocity v, while the disc started rotating coun-
  terclockwise with a constant angular acceleration 13 (the initial angu-
  lar velocity is equal to zero);

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