Physics

posted by .

You are riding a merry-go-round on the rim which is turning counterclockwise at a constant angular speed of 0.5 rad/s.  Your dog sees you at the 12 o'clock position when he is at the 3 o'clock position.  He starts running counterclockwise from rest with an angular acceleration of 0.31 rad/s2.  The merry-go-round has a radius of 3.36 m.
 
a) When does your dog first catch up to you?

b) How fast is your dog running (in m/s) at the instant you computed in part a?

  • Physics -

    Man: φ=ω•t
    Dog: φ=ε•t²/2
    ω•t= ε•t²/2
    t=2 ω/ ε=2•0.5/0.31 =3.23 s
    ω(dog) = ε•t=0.31•3.23= 1 rad/s

  • Physics -

    It gives me the wrong answer for some reason.

    Thanks for the help though! I appreciate it.

  • Physics -

    Man: φ =ω•t
    Dog: φ –π/2=ε•t²/2
    ω•t= ε•t²/2 +π/2
    ε•t² -2 ω•t+π=0
    t={2±sqrt(4-2•3.14•0.31}/2•0.31
    t1=3.74 s, t2 = 1.48 s
    ω(dog) = ε•t=0.31•1.48= 0.459 rad/s

Respond to this Question

First Name
School Subject
Your Answer

Similar Questions

  1. physics

    A 0.21 kg ball on a string is whirled on a vertical circle at a constant speed. When the ball is at the three o'clock position, the tension is 18 N. (c) Is the tension in the string greater when the ball is at the twelve o'clock position …
  2. physics

    A ball is lodged in a hole in the floor near the outside edge of a merry-go-round that is turning at constant speed. Which kinematic variable or variables change with time, assuming that the position is measured from an origin at the …
  3. Physics

    A ball is lodged in a hole in the floor near the outside edge of a merry-go-round that is turning at constant speed. Which kinematic variable or variables change with time, assuming that the position is measured from an origin at the …
  4. Physics

    A ball is lodged in a hole in the floor near the outside edge of a merry-go-round that is turning at constant speed. Which kinematic variable or variables change with time, assuming that the position is measured from an origin at the …
  5. Physics

    In a playground, there is a small merry-go-round of radius 1.20 m and mass 190 kg. Its radius of gyration (see Problem 85 of Chapter 10) is 91.0 cm. A child of mass 44.0 kg runs at a speed of 4.50 m/s along a path that is tangent to …
  6. physics

    A merry-go-round is stationary. A dog is running on the ground just outside its circumference, moving with a constant angular speed of 0.705 rad/s. The dog does not change his pace when he sees what he has been looking for: a bone …
  7. physics

    A dog sits 3.0 m from the center of a merry- go-round. a) If the dog undergoes a 1.2 m/s2 cen- tripetal acceleration, what is the dog’s linear speed?
  8. physics

    A small object with mass 4.05 kg moves counterclockwise with constant speed 1.70 rad/s in a circle of radius 3.15 m centered at the origin. It starts at the point with position vector 3.15 m. Then it undergoes an angular displacement …
  9. Physics

    A person exerts a tangential force of 34.8 N on the rim of a disk-shaped merry-go-round of radius 2.60 m and mass 152 kg. If the merry-go-round starts at rest, what is its angular speed after the person has rotated it through an angle …
  10. Physics

    a merry-go-round of radius 2 m and a moment of inertia 651 kgmm is stationary. a 78 kg woman runs at 1.6 m/s and jumps on tangentially to the rim of the merry-go-round. what is the final angular velocity of the merry-go-round?

More Similar Questions