VDU_Physics_1_006  
Solved UniversityPhysics ProblemsPhysics 1. Mechanics: Circular MotionJavier Montenegro Joo jmj@VirtualDynamics.Org
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Circular motion.  
(1)
A 10cm diameter
frictionless disk is rotating about its axis at 1000 rpm. Suddenly
while the disk is rotating, a particle located at a distance of half
radius gets released and it is triggered. Determine the shooting speed
of this particle. Solution. The angular speed of the disk is the same at any radial distance, hence the initial velocity of the released particle is:


[01234]


(2)
A 120 gr ball is
tied to the end of a string of 3 m which is rotating with its other end
fixed to a rotating shaft. The ball describes a circular orbit and moves
with an acceleration of 10 m/s^{2 }. When the acceleration
vector makes an angle of 25^{o} with rope, calculate (a) radial
acceleration (b) tangential acceleration (c) speed of the ball.
Solution.




(5)
Two wheels whose diameters are 40 cm and 60 cm, respectively, are on the
same plane and they are separated. Both wheels are connected by a belt
passing around their edges. Determine the angular velocity of the larger
wheel when the smaller wheel rotates at 600 rpm. Calculate the distance
traveled during 7.5 min by a point of the belt. Solution. The tangential velocity of both wheels is the same, then:


[56789]


Accelerated Circular Motion.  
(3)
A disk of 2.5 kg and
1 m diameter is rotating at 3000 rpm when it is disconnected from the
source of energy that keeps it rotating. For the moment just before disconnection
calculate: (a) angular speed of the disc (b) tangential speed of a point
on the edge of the disc, (c) centripetal acceleration of a point on the
edge of the disc (d) If the disk stops 30 s after disconnection,
determine how many turns are completed during that time.
Solution.


(4)
A 2.50 m diameter disk starts rotating with an angular speed of 1.75 rad/s
and a constant acceleration of 1.60 rad/s^{2 }. For a dot at
the edge of the disk and for 1.50s after initiated the motion,
calculate: (a) Displacement, (b) Angular velocity, (c) Tangential
velocity, (d) Magnitude of the acceleration vector, (e) Angle between
acceleration and radius. Solution.

