Conservation of Linear and Angular Momentum

In this experiment, we will study about the conservation between a object's linear velocity and its angular momentum. Therefore, we will try doing the experiment to expect the angular speed of the disk after the ball impact the disk in order to to in order to study the angular momentum and linear momentum of a ball in collision.
First of all, professor set the equipment to know the velocity of the ball(0.0247 kg) before collision as below picture shows:

We determined the distance between end of track and the ground is 0.955 m and the distance of horizontal travel of the ball is 0.552 m.

From this function, we can get the time it take, and we can make horizontal distance divide the time to get the velocity. And then, we get 1.1824 m/s.

After getting the velocity and the mass of the ball, we are able to know the linear momentum of the ball.

Next section is determining the angular momentum of the ball, so we need to know the disk's angular velocity and inertia after collision. However, we decide to find the inertia first. For finding the inertia, we will use a string that attended to a hanging mass wrapping around the top pulley.And then, let it drop down and measure the angular acceleration.

angular acceleration: 5.6365 rad/s^2

top pulley's radius: 0.025 m

mass of ball: 0.0247 kg

And we use this function to get the inertia:

After we substitute data:

And then, we are able to find the angular speed after collision:

Thus, we expect the angular speed is 1.957 rad/s.

But the real angular speed is 1.775 rad/s.

Conclusion: the reason why the expect one is bigger than real one is the friction and the disk is not perfect friction-less. However, this lab helps us recognize the conservation of linear and angular momentum.