College Physics
posted by Taylor .
A 40 kg child is standing on the edge of a merrygoround in a playground. Before they were deemed too dangerous, these were quite common. They were just huge rotating platforms you could sit on while someone spun you around in uniform circular motion until you screamed in terror (or possibly got sick). At any rate, let us assume the merry goround is a rotating disk of radius R = 1.5m and inertia M = 100kg and the child is a point particle located at the edge of the disk. The merrygoround is initially at rest. The child’s brother tosses him a basketball from across the playground. Assume the basketball has a mass of 0.62kg and is thrown with a velocity of 20m/s perpendicular to the radius of the merrygoround at the point where the child catches it.
(a)[7 pt(s) ]Assume that there is no friction in the axle of the merrygoround, so it can rotate freely. Assume that there is a lot of friction between the child and the merrygoround, so that he does not slide as he catches the ball. What is the final angular velocity of the merrygoround after the child catches the ball?
(b)[4 pt(s) ]How much work is done on the merrygoround? What does this work?
(c)[3 pt(s) ]Draw the workenergy diagram to express the change in energy of the system consisting of only the merrygoround.
(d)[4 pt(s) ]Does the merrygoround do any work on the ball? On the child? How much?
(e)[3 pt(s) ]What is the centripetal force acting on the ball after the child catches it?

College Physics 
Elena
a. The linear momentum of the ball
(m(o) – 0.64 kg), v =20 m/s) is
p = m(o)•v .
The angular momentum is
L = m(o)•v•R .
On the other hand, the angular momentum is
L =I•ω,
where the total moment of inertia (merrygoround + the child) is
I = mR^2 +MR^2/2.
m(o)•v•R =( mR^2 +MR^2/2) •ω,
ω = m(o)•v/(R•(m+M/2)) = 0.092 rad/s.
b.The work is the change of the rotational kinetic energy
W = ΔKE = I•ω^2/2 = (mR^2 +MR^2/2) •ω^2/2 =202.5•(0.092)^2/2 = 34.28 J.
c. 
d. 
e.F =m•a=m• ω^2•R =0.062•(0.092)^2•1.5 = 7.87•10^3 N.
Respond to this Question
Similar Questions

Physics Inertia : Merrygoround
A playground merrygoround of radius 1.96 m has a moment of inertia 335 kg m2 and is rotating at 12.3 rev/min. A child with mass 43.1 kg jumps on the edge of the merrygoround. What is the new moment of inertia of the merrygoround … 
Physics: merrygoround question
A playground merrygoround of radius 1.92 m has a moment of inertia 411 kg m2 and is rotating at 10.4 rev/min. A child with mass 38.3 kg jumps on the edge of the merrygoround. Assuming that the boy's initial speed is negligible, … 
Physics
A merrygoround is at rest before a child pushes it so that it rotates with a constant angular acceleration for 38.0 s. When the child stops pushing, the merrygoround is rotating at 1.20 rad/s. How many revolutions did the child … 
College Physics
A freely rotating merrygoround on a playground has a moment of inertia of 312 kgm2 and a radius of R=2.5 m. It is rotating with ω0=2.8 rad/s when a kid of mass 45 kg is standing on its outer rim. Neglecting friction, what is … 
physics
A 44.8 child is standing on the outer edge of a merrygoround that has moment of inertia 981 and radius 2.40 . The entire system is initially rotating at 0.180 . Find the angular velocity if the child moves to a final position 1.10 … 
Physics
A playground merrygoround of radius R = 2.15 m has a moment of inertia of I = 256 kg * m2 and is rotating at 10.9 revolutions/min about a frictionless vertical axle. Facing the axle, a 29.6 kg child hops onto the merrygoround and … 
physics
a child sits on the edge of a spinning merrygoround 3.2 m from its center. The coefficient of static friction between the child's bottom and the surface of the merrygoround is .8. Find the maximum rate in revolutions per seconds, … 
physics
A playground merrygoround of radius 2.00 m has a moment of inertia I = 255 kg·m2 and is rotating about a frictionless vertical axle. As a child of mass 25.0 kg stands at a distance of 1.00 m from the axle, the system (merrygoround … 
Physics
A playground merrygoround of radius R = 1.92m has a moment of inertia of I = 221kgm^2 and is rotating at 14.0rev/min about a frictionless vertical axle. Facing the axle, a 29.8kg child hops onto the merrygoround and manages to … 
physics
A playground merrygoround of radius R = 1.1 m has a moment of inertia of I = 280 kg*m^2. and is rotating at a rate of ω = 9 rev/min around a frictionless vertical axis. Facing the axle, a 37 kg child hops onto the merrygoround …