- #1
EndoBendo
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A horizontal vinyl record of mass 0.10 kg and radius 0.1 m rotates freely about a vertical axis through its center with an angular speed of 4.7 rad/s. The rotational inertia of the record about its axis of rotation is 0.0005 kg*m^2. A wad of wet putty of mass 0.020 kg drops vertically onto the record from above and sticks to the edge of the record. What is the angular speed of the record immediately after the putty sticks to it?
Did I do this correctly?? I really struggled to get this lol
Angular momentum = moment of inertia * angular velocity
Moment of inertia of a solid cylinder, like the record = ½ * mass * radius^2
I = ½ * 0.1 * 0.1^2 = 0.0005
Initial angular momentum = 0.0005 * 4.7
Moment of inertia putty = mass * radius^2
I = 0.02 * 0.1^2 = 0.0002
Total moment of inertia after the sticks to the edge of the record = Sum of I’s = 0.0007
Final angular momentum = 0.0007 * final angular velocity
Final angular momentum = Initial angular momentum
0.0007 * final angular velocity = 0.0005 * 4.7
new angular velcoity = 3.36 rad/s
Did I do this correctly?? I really struggled to get this lol
Angular momentum = moment of inertia * angular velocity
Moment of inertia of a solid cylinder, like the record = ½ * mass * radius^2
I = ½ * 0.1 * 0.1^2 = 0.0005
Initial angular momentum = 0.0005 * 4.7
Moment of inertia putty = mass * radius^2
I = 0.02 * 0.1^2 = 0.0002
Total moment of inertia after the sticks to the edge of the record = Sum of I’s = 0.0007
Final angular momentum = 0.0007 * final angular velocity
Final angular momentum = Initial angular momentum
0.0007 * final angular velocity = 0.0005 * 4.7
new angular velcoity = 3.36 rad/s