2 Masses on a Pulley - Torque Demonstration

Summary

In this physics lesson, students tackle a pulley system problem involving two hanging masses, a frictionless pulley, and its rotational inertia. The group works through the calculation of the angular acceleration of the pulley and the forces of tension in each string. The importance of considering the mass and rotational inertia of the pulley is emphasized, as it affects the tensions on either side of the pulley. Along the way, common mistakes are discussed, and the correct approach of relating linear and angular accelerations is highlighted. The final results include angular acceleration of 2.67 radians per second squared and tension forces of 0.991 N and 1.94 N.

Takeaways

• 😀 The pulley system consists of two masses (0.100 kg and 0.200 kg) hanging on either side of a frictionless pulley with a known rotational inertia and radius.
• 😀 The rotational inertia of the pulley is 0.0137 kg·m² and its radius is 0.0385 meters.
• 😀 The problem involves calculating the angular acceleration of the pulley and the force of tension in each string attached to the masses.
• 😀 The two forces of tension on either side of the pulley are not equal due to the pulley having mass and rotational inertia, which requires a net torque to cause angular acceleration.
• 😀 Free body diagrams were used to analyze the forces acting on the pulley and the hanging masses, including tension forces and gravitational forces.
• 😀 While the string is the same, the tension in each part is different because the pulley has mass, causing unequal tension on both sides.
• 😀 The net torque on the pulley is the difference between the torques caused by the two tensions, and it leads to angular acceleration.
• 😀 The linear acceleration of the hanging masses is equal to the tangential acceleration at the rim of the pulley, which links the angular and linear accelerations.
• 😀 The angular acceleration of the pulley was calculated using the formula involving rotational inertia, mass differences, and pulley radius, yielding a result of 2.67 radians per second squared.
• 😀 The experimentally measured angular acceleration was 2.43 radians per second squared, with a 9.03% error from the theoretical calculation.
• 😀 When solving for the forces of tension, the tension in each string was calculated separately, taking into account the masses and the pulley’s rotational acceleration, yielding 0.991 N for tension 1 and 1.94 N for tension 2.

Q & A

What is the setup of the physics problem discussed in the video?

The problem involves two masses, 0.100 kg and 0.200 kg, hanging from either side of a frictionless pulley. The pulley has a rotational inertia of 0.0137 kg·m² and a radius of 0.0385 meters.

Why are the forces of tension not equal on either side of the pulley?

The forces of tension are not equal because the pulley has mass and rotational inertia. A net torque is required to angularly accelerate the pulley, meaning the tension forces on both sides must differ.

What assumption simplifies the tension forces in some pulley problems?

In simplified pulley problems, where the pulley is assumed to have negligible mass and friction, the two forces of tension would be considered equal.

What is the significance of defining clockwise as the positive direction in the problem?

By defining clockwise as the positive direction, it helps in consistently summing torques and forces, ensuring correct directionality when calculating angular acceleration and tension forces.

How does the rotational inertia of the pulley affect the system?

The rotational inertia of the pulley causes a difference in the tension forces on either side, as the pulley requires a net torque to rotate, leading to unequal tensions.

Why do the free body diagrams not include the force of gravity or normal force for the pulley?

The force of gravity and normal force acting on the pulley do not cause any torque since they act at the center of mass, which is the axis of rotation. Therefore, these forces are not part of the torque calculations.

What is the relationship between linear acceleration and angular acceleration in this system?

The linear acceleration of the hanging masses is equal to the tangential acceleration of the rim of the pulley, which is the radius of the pulley multiplied by its angular acceleration.

What formula is used to calculate the angular acceleration of the pulley?

The formula for angular acceleration is: angular acceleration = (gravitational acceleration × pulley radius × (mass 2 - mass 1)) / (rotational inertia + pulley radius² × (mass 1 + mass 2)).

What does the comparison between measured and predicted angular acceleration reveal?

The measured angular acceleration was 2.43 radians per second squared, while the predicted value was 2.67 radians per second squared. The percentage difference was -9.03%, indicating the measured value was slightly lower.

What common mistakes do students make when solving pulley problems like this?

Students often make two main mistakes: summing the torques for the entire system at once, or summing the forces for the entire system in the positive direction. Both methods incorrectly assume the system as a whole has rotational inertia or uniform acceleration.