1. A rigid rod of mass M and length L is free to pivot on a horizontal axle about its center. It hangs vertically and gently rests on a frictionless surface. A sticky ball of mass m travelling horizontally toward the rod with velocity v, collides with the rod and sticks to the bottom end. The goal of this problem is to find the maximum angle through which the rod rotates after the collision. M ) Sketch a picture of the rod + ball system after the collision. Label your diagram and list а. LA any knowns or unknowns for the problem. b. Determine the moment of inertia for the ball + rod system after the collision. Using this, write down the angular momentum conservation equation about the rod's pivot point. Determine a symbolic expression for velocity of the ball after the collision. с. d. Determine a symbolic expression for the maximum angle, measured from the vertical, through which the rod rotates. Suppose L = 30 cm, M = 75 g, m = 10 g, v. = 2.5 m/s. What is the maximal angle through which the rod rotates? What height above the frictionless surface does this correspond to?
1. A rigid rod of mass M and length L is free to pivot on a horizontal axle about its center. It hangs vertically and gently rests on a frictionless surface. A sticky ball of mass m travelling horizontally toward the rod with velocity v, collides with the rod and sticks to the bottom end. The goal of this problem is to find the maximum angle through which the rod rotates after the collision. M ) Sketch a picture of the rod + ball system after the collision. Label your diagram and list а. LA any knowns or unknowns for the problem. b. Determine the moment of inertia for the ball + rod system after the collision. Using this, write down the angular momentum conservation equation about the rod's pivot point. Determine a symbolic expression for velocity of the ball after the collision. с. d. Determine a symbolic expression for the maximum angle, measured from the vertical, through which the rod rotates. Suppose L = 30 cm, M = 75 g, m = 10 g, v. = 2.5 m/s. What is the maximal angle through which the rod rotates? What height above the frictionless surface does this correspond to?
1. A rigid rod of mass M and length L is free to pivot on a horizontal axle about its center. It hangs vertically and gently rests on a frictionless surface. A sticky ball of mass m travelling horizontally toward the rod with velocity v, collides with the rod and sticks to the bottom end. The goal of this problem is to find the maximum angle through which the rod rotates after the collision. M ) Sketch a picture of the rod + ball system after the collision. Label your diagram and list а. LA any knowns or unknowns for the problem. b. Determine the moment of inertia for the ball + rod system after the collision. Using this, write down the angular momentum conservation equation about the rod's pivot point. Determine a symbolic expression for velocity of the ball after the collision. с. d. Determine a symbolic expression for the maximum angle, measured from the vertical, through which the rod rotates. Suppose L = 30 cm, M = 75 g, m = 10 g, v. = 2.5 m/s. What is the maximal angle through which the rod rotates? What height above the frictionless surface does this correspond to?
Please Label Variables in explanation (eg. L = angular momentum)
Transcribed Image Text:1. A rigid rod of mass M and length L is free to pivot on a horizontal axle about its center. It hangs
vertically and gently rests on a frictionless surface. A sticky ball of mass m travelling horizontally
toward the rod with velocity v. collides with the rod and sticks to the bottom end. The goal of this
problem is to find the maximum angle through which the rod rotates after the collision.
M
Vo
а.
:) Sketch a picture of the rod + ball system after the collision. Label your diagram and list
any knowns or unknowns for the problem.
Determine the moment of inertia for the ball+ rod system after the collision. Using
this, write down the angular momentum conservation equation about the rod's pivot point.
b.
Determine a symbolic expression for velocity of the ball after the collision.
с.
d.
Determine a symbolic expression for the maximum angle, measured from the vertical,
through which the rod rotates.
e..
, Suppose L = 30 cm, M = 75 g, m = 10 g, v. = 2.5 m/s. What is the maximal angle
through which the rod rotates? What height above the frictionless surface does this correspond to?
Definition Definition Product of the moment of inertia and angular velocity of the rotating body: (L) = Iω Angular momentum is a vector quantity, and it has both magnitude and direction. The magnitude of angular momentum is represented by the length of the vector, and the direction is the same as the direction of angular velocity.
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