Objective: The objective of this laboratory was to theoretically calculate the moment of inertia of a disk and a ring and then to verify the moment of inertia for both objects through experiment. This laboratory shows that while the theoretical is not within the uncertainty of the experimental, both values are extremely similar to each other.
Data and Analysis:
Data:
Table 1: The Angular Acceleration of No Ring and Ring
Trial No Ring Ring
5g 4.57 ± 0.005 rad/s2 1.32 ± 0.005 rad/s2
10g 13.16 ± 0.005 rad/s2 3.09 ± 0.005 rad/s2
15g 20.45 ± 0.005 rad/s2 4.83 ± 0.005 rad/s2
20g 27.89 ± 0.005 rad/s2 6.60 ± 0.005 rad/s2
25g 35.65 ± 0.005 rad/s2 8.35 ± 0.005 rad/s2 Table 2: The Average Experimental and Theoretical Moment of Inertia for No
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This calculation will be done later on. After using equation 1 to find the experimental moment of inertia, the average and standard deviation of the five trials for No Ring and Ring were calculated using Excel commands for average and standard deviation. The averages will be used later on in order to calculate the experimental moment of inertia for the ring. In the next step, the theoretical moment of inertia was calculated for the disk by using equation 2.
I_disk^th=1/2 M_d R_d^2 (2)
In the equation above, the I_disk^th is the theoretical moment of inertia of the disk, M_d is the mass of the disk, Rd is the radius of the disk. Next, the theoretical moment of inertia of the Ring was calculated using equation 3 below.
I_ring^th=1/2 M_r (R_1^2+R_2^2) (3)
In the equation above, I_ring^this the theoretical moment of inertia of the Ring, Mr is the mass of the ring, R_1^2 is the inner radius of the ring, and R_2^2 is the outer radius of the ring. In order to compare the experimental and theoretical moments of inertia of the Ring, the experimental moment of inertia of the ring alone has to be calculated. It is given that the experimental moment of the system equals to the experimental moment of inertia of the ring plus the experimental moment of inertia of the disk. The experimental moment of inertia can be found by solving
Determine the volume of the magnet and metal bolt to +/- 0.1 mL using units and sig figs carefully. Measure the mass and calculate the density of the magnet and metal bolt using the correct significant figures and units. Show work for full credit. (2 points)
We can derive our equation from the equation of centripetal force by doing the following;
Set the radius to 2.0 m, the mass to 1.0 kg, and the velocity to 10.0 m/s.
The objective of this lab was to explore the behavior of centripetal acceleration and identify the relationships between the acceleration and several forces acting on the object.
Locate the force string and use the hooked end to connect the force string to the other side of the spinning mass. Guide the force string over the pulley. Suspend the mass hanger plus an additional 0.55 kg of mass, so that m= 0.6 kg. Ensure that the weight hanger does not touch the table top. This hanging mass will be referred to as the force mass from now on, and is used to set the centripetal force, Fc. The force Fc is equal to the force mass, in kg, multiplied by gravity. Calculate this value and record it onto Data Sheet C. Adjust the tension knob so that the tip of the spinning mass is directly above the
First, we will set up the force table. The table comes in three separate pieces the base, stand and table once we connect and fasten all three parts we must use a circular level to make sure the table is balanced. If the force table isn’t balanced then we must adjust the base’s feet to the appropriate levels on each leg till the bubble on the level is centered. We must then assign where the positive & negative x, y axis are on the force table as a point of reference and label them with tape .Then for part I we must apply 1.96 N in the positive x – direction, and 2.94 N in the positive y-direction then we must balance the two with a third force and record the magnitude and direction of it and a draw a diagram showing all three forces. Part II
$\boldsymbol{P_{DC,max}}$ & $\frac{V_{DD}^{2}}{R_{opt}}$ & $\frac{2V_{DD}^{2}}{\pi R_{opt}}$& $\frac{V_{DD}.I_{rf}}{\pi}.[sin\theta - \theta cos\theta]$ & $\frac{V_{DD}.I_{rf}}{\pi}.[sin\theta - \theta cos\theta]$ \\ \hline
Introduction During this lab you will become more familiar with the concepts of torque. The purpose of this lab is to determine if the rotational equilibrium condition, Στ = 0, holds experimentally. Equipment Meter stick (1) - no metal ends Fulcrum (1) Clamps (4) Weight Hanger (1) Mass Set (1) Digital Scale (1)
What is the question asking you to identify? This question is asking to clearly identify centripetal force.
Fig. 1. (a) Schematic view of the structure at rest. (b) Schematic view under external acceleration
In the most common form of 1-DOF torsional plant, friction is taken as being viscous. Applying Newton's second law to the attached rotating disk using free body diagram method then following up with differential equation and the deducing:
Contrary to highest acceleration signal gotten at take-off, the gyroscope signal shows the highest change in signal at landing impact. For all previously detected times and derivative of the gyroscope signal will be analysed with the interval {ta -1s] to ta +1s]. therefore, L-1 norm of the gyroscope
where P is the estimated power generated, B is the magnetic field of the accretion disk, and RS is the Schwarzschild radius of the black hole.
Where P is the applied force, L is the length of beam, E is the modulus of elasticity of aluminum, and I is the moment of Inertia.
Definition Parallel Axis Theorem on Product of Inertia Moments of Inertia About an Inclined Axes Principal Moments of Inertia Mohr’s Circle for Second Moment of Areas