1. A lawn merry-go-round with radius 2.2 m has a moment of inertia 231 kg⋅m2 and is rotating at 13 rev/min about a fric

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1. A lawn merry-go-round with radius 2.2 m has a moment of
inertia 231 kg⋅m2 and is rotating at 13 rev/min about a
frictionless vertical axis. Facing the spindle, a 31-kg boy jumps
onto the carousel and manages to sit on the edge. What is the new
angular speed (rev/min) of the carousel? Give your answer to one
decimal place.
2. A boy of mass 94 kg runs at a speed of 20 m/s and jumps
into a car as shown in the figure below. The car is initially at
rest. If the speed of the car with the boy on it is 4.5 m/s, what
is the mass (in kg) of the car? From your answer without
decimals.
3.A uranium nucleus (mass 238 units) at rest decays into a
helium nucleus (mass 4.0 units) and a thorium nucleus (mass 234
units). If the velocity of the helium nucleus is 3412767( m/s, what
is the magnitude of the velocity of the thorium nucleus? Give your
answer to one decimal place
4. Three children push a circular platform (M = 4 kg) in a
playground. The platform has a radius of 3.89 m. The figure shows,
two boys pull with equal forces of 40.0 N in an attempt to rotate
the platform clockwise. The third child applies a force of 60 N as
shown. What is the angular acceleration in rad/s2) of the platform?
Give your answer to 2 decimal places.