11 May 2015. Inertia and Frictional Torque.

Purpose

1. To find the frictional torque of an apparatus designed by finding the moment of inertia of the wheel.
2. From that, we will calculate the inertia for the wheel, and then use it to determine how long a cart hanging off the wheel by a string would take to go a meter-long ramp.

Apparatus:

The wheel. This is the steel cast in one piece with the cylinder axle protruding on both sides. Imagine the object as three pieces: a solid disk, and two cylinders on the sides. The total mass of this is 4.840 kg.

Procedure and Data analysis

for this lab blog, the procedure and data analysis will be described individually under one part section. Since there are two parts of this experiment.


Part 1 (finding the friction torque)

Procedure

1. We need to measure the radius and all the mass needed to find the inertia.
2. Then we also need to measure the angular deacceleration, which is also caused by the friction torque.
3. To find this, we need to do video capture.
4. We line up the camera, then do add point series at every same point when the wheel has finished rotating one full rotation.
5. Note that, if there is no friction, the wheel will turn infinitely, but of course it doesn't. So, there must the angular deacceleration that we mentioned.

Data Analysis

• Now, we let's find the inertia first.
• We know that the whole mass is 4.840 kg (written there). We need to divide this mass as three pieces: a solid disk, and two cylinders on the sides. Let's do this.
• We already measure all the radius of this disk as follow.
• Then we calculate the volume of each one, and compare it to the mass. Remember that mass and volume has a linear relationship.

• So, we got our small cylinders masses as .653 kg and the solid disk 4.187 kg.
• And the total inertia is the combined inertia of both disk as follow.

• Next, let's find the angular deacceleration. When we do the video capture analysis (explained in the procedure section), we will have the delta t time, when each disk is finished rotating one full rotation. And from that we can determine the angular speed, which will be slower each time due to friction.
• We plot omega vs time to find the slope as our angular acceleration.

• Next, we transformed this line equation into:

• Yes! We finally found our torque friction in this wheel.

Part 2 (finding the time when a cart attached to this wheel by string will travelled 1m)

Procedure

1. Set up the ramp as the picture shown.

2. Now, attached a cart to the smaller wheel with a string.
3. Do not forget to weigh the mass of the cart and measure the angle of the ramp.
4. Then give a gentle push to the wheel (not to hard, not to soft), making the cart goes down.
5. When the cart stars going down, hit the stopwatch, and press it again when the cart reaches 1 m long.
6. Do this three times and compare it with the true calculated value.

Data Analysis

• Now, let's calculate the calculated true value.

• Now, from the calculated value, we should get 7.34 s for the cart to go 1-m long.
• Let's calculate the percent error.

• The percent error is under 5 percent.

Conclusions

•  We manage to calculate the friction torque.

• And from there, calculate the time of an object that is attached to the wheel by considering the equation of the torque, angular acceleration, and inertia.

• There are some small errors in this experiment that comes from;

• When we add point series, we did not really click it precisely. This will alter the velocity and the position of angular movement.

• Friction from the ramp, but we ignore that.

• Some uncertainties when calculating the radius and others.

• Uncertainties when calculating the time with a stopwatch.