A disk slides toward a motionless stick on a frictionless surface (figure below)

Question

A disk slides toward a motionless stick on a frictionless surface (figure below). The disk strikes and adheres to the stick and they rotate together, pivoting around the nail. Angular momentum is conserved for this inelastic collision because the surface is frictionless and the unbalanced external force at the nail exerts no torque.

Consider a situation where the disk has a mass of 50.5 g and an initial velocity of 32.5 m/s when it strikes the stick that is 1.30 m long and 2.05 kg at a distance of 0.100 m from the nail.

(a)

What is the angular velocity (in rad/s) of the two after the collision? (Enter the magnitude.)

(b)

What is the kinetic energy (in J) before and after the collision?

(c)

What is the total linear momentum (in kg · m/s) before and after the collision? (Enter the magnitude.)

Explanation / Answer

a)

Is = moment of inertia of stick = ML2/3 = (2.05) (1.30)2/3 = 1.2 kgm2

m = mass of disk = 50.5 g = 0.0505 kg

v = speed of disk before collision = 32.5 m/s

w = angular velocity of the combination after collision

using conservation of angular momentum

m v L = (Is + m L2) w

(0.0505) (32.5) (1.30) = (1.2 + (0.0505) (1.30)2) w

w = 1.7 rad/s

b)

Kbefore = (0.5) m v2 = (0.5) (0.0505) (32.5)2 = 26.7 J

Kafter = (0.5) (Is + m L2) w2 = (0.5) (1.2 + (0.0505) (1.30)2) (1.7)2 = 1.86 J

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