A merry-go-round in a playground (spinning horizontal disk) of mass M and radius R is initially rotating inthe x/y plane at a constantω0around a fixed vertical axis through the middle of the disk. A girl of mass m runstowards italong a path that is tangent to the rim and then jumps on the rim and holds on. The disk spinsfasterafter she jumps on. Treat the girl as a point mass.a) Choose one: Which of the following is conserved for the disk+girl system before and after she jumps on? (i) mechanical energy, ii) angular momentum, iii) linear momentum. iv) 2 or more of the above. b) Draw an overhead sketch of the disk with the disk rotating such that ω0 is in the +z direction (out). Show thevelocity vector of thegirl right before she jumps on. Solve for the necessary speed v that she must have in order for the disk to tripleits angular velocity after she jumps on. Your expression should depend on ω0, m, M, andR. Simplify it as much as you can
Rigid Body
A rigid body is an object which does not change its shape or undergo any significant deformation due to an external force or movement. Mathematically speaking, the distance between any two points inside the body doesn't change in any situation.
Rigid Body Dynamics
Rigid bodies are defined as inelastic shapes with negligible deformation, giving them an unchanging center of mass. It is also generally assumed that the mass of a rigid body is uniformly distributed. This property of rigid bodies comes in handy when we deal with concepts like momentum, angular momentum, force and torque. The study of these properties – viz., force, torque, momentum, and angular momentum – of a rigid body, is collectively known as rigid body dynamics (RBD).
PLEASE SOME ANSWER THIS ASAP AND SHOW ALL THE WORK PLS
A merry-go-round in a playground (spinning horizontal disk) of mass M and radius R is initially rotating inthe x/y plane at a constantω0around a fixed vertical axis through the middle of the disk. A girl of mass m runstowards italong a path that is tangent to the rim and then jumps on the rim and holds on. The disk spinsfasterafter she jumps on. Treat the girl as a point mass.a) Choose one: Which of the following is conserved for the disk+girl system before and after she jumps on? (i) mechanical energy, ii)
b) Draw an overhead sketch of the disk with the disk rotating such that ω0 is in the +z direction (out). Show thevelocity vector of thegirl right before she jumps on. Solve for the necessary speed v that she must have in order for the disk to tripleits
a)
ii) Angular momentum is conserved.
Explanation:
This is the case of the inelastic collision. So, the mechanical energy of the system cannot be conserved.
The angular momentum of the system is conserved because the torque of the external forces is equal to zero.
The linear momentum of the system is not conserved because the net external force on the system is not zero. Here, the forces involved are the frictional force between the feet of the girl and the merry-go-round and the force exerted by the ground. These both force would be in the plane of the merry-go-round opposite to each other.
b)
The required figure is given below.
Here, the Z-axis is perpendicular to the plane of the merry-go-round.
Step by step
Solved in 2 steps with 2 images
