Physics 1111 Fall 2020 Name Quiz ✓ Solved

Physics 1111 Fall 2020 Name Quiz

Consider a 5.0 kg solid disk with a 2.0 m radius, which is initially spinning on its central axis in a counterclockwise direction with an angular speed of 5.0 rad/s. What is the angular momentum of this spinning disk?

Now, a second object, which is not initially rotating, is dropped on top of the first and they stick together. The final angular speed of the two objects stuck together is 2.0 rad/s in the same counterclockwise direction. What is the magnitude of the moment of inertia of the second object?

What was the initial rotational kinetic energy of the spinning disk in question 1 before the object from question 2 was dropped?

Paper For Above Instructions

The angular momentum (L) of a solid disk can be calculated using the formula:

L = I * ω

Where:

I = moment of inertia of the disk

ω = angular speed

The moment of inertia (I) of a solid disk is given by the formula:

I = (1/2) M R2

Substituting the values:

M = 5.0 kg

R = 2.0 m

Thus:

I = (1/2) 5.0 kg (2.0 m)2 = (1/2) 5.0 4 = 10 kg·m2

Now, we substitute I into the angular momentum formula:

L = 10 kg·m2 * 5.0 rad/s = 50 kg·m2/s

Therefore, the angular momentum of the spinning disk is:

Angular Momentum: 50 kg·m2/s

Next, we need to calculate the moment of inertia (Ifinal) of the combined system (disk + second object) after the second object is dropped on the first one. The angular speed of the combined system is given as 2.0 rad/s.

Using the conservation of angular momentum, since no external torque acts on the system:

Linitial = Lfinal

We already found Linitial = 50 kg·m2/s. For the final angular momentum, we can write:

Lfinal = Ifinal * ωfinal

Where:

ωfinal = 2.0 rad/s

Setting them equal gives:

50 kg·m2/s = Ifinal * 2.0 rad/s

Solving for Ifinal:

Ifinal = 50 kg·m2/s / 2.0 rad/s = 25 kg·m2

Now we can find the moment of inertia of the second object (Isecond) by subtracting the moment of inertia of the first object from the final total:

Isecond = Ifinal - Idisk = 25 kg·m2 - 10 kg·m2 = 15 kg·m2

Moment of Inertia of the Second Object: 15 kg·m2

Lastly, we need to calculate the initial rotational kinetic energy (Kinitial) of the spinning disk before the second object was added. The kinetic energy can be calculated using the formula:

K = (1/2) I ω2

Substituting the values we previously calculated:

Kinitial = (1/2) 10 kg·m2 (5 rad/s)2

Kinitial = (1/2) 10 25 = 125 J

Initial Rotational Kinetic Energy: 125 Joules

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