Torque & Rotational Equilibrium
Interactively balance forces on a rigid lever by placing masses at different distances from the pivot. Observe torque magnitudes and directions, and understand the condition for rotational equilibrium.
WHAT IS TORQUE?
Torque (\tau) is the rotational equivalent of force. It is a measure of how much a force acting on an object causes that object to rotate about an axis. Torque depends on three factors: the magnitude of the **force** (), the **lever arm** distance from the pivot (), and the **angle** (\theta) at which the force is applied. To maximize torque, you should apply force as far from the pivot as possible and perpendicular to the lever arm.
ROTATIONAL EQUILIBRIUM
An object is in **mechanical equilibrium** if two conditions are met: the net force is zero (translational equilibrium) AND the **net torque** is zero (rotational equilibrium). In AP Physics 1, this often involves a 'see-saw' or a beam where clockwise torques must perfectly balance counter-clockwise torques ().
HOW TO USE THIS VISUALIZATION
1. **The Balance Beam**: Drag weights of different masses onto the beam. 2. **Adjust Position**: Change the distance of the masses from the pivot. Observe how a smaller mass further away can balance a larger mass closer to the center. 3. **Calculate Torque**: Watch the live readout for . Check that when the beam is horizontal. 4. **Angle Control**: Change the angle of an applied force. Notice that only the perpendicular component () contributes to the torque.
CORE FORMULAS
AP EXAM CONNECTION
Unit: Unit 5: Torque and Rotational Dynamics (Topic 5.1)
Learning Objective: 5.1.1
COMMON MISCONCEPTIONS
- Thinking that a net force of zero implies a net torque of zero (and vice-versa).
- Forgetting to account for the angle of the applied force.
- Neglecting the weight of the beam itself when it is not "massless."
KEY TAKEAWAYS
- Torque is the "twist" caused by a force.
- Lever arm distance is as important as the force magnitude.
- Equilibrium requires balanced forces AND balanced torques.
- Torque is maximum when force is perpendicular to the lever arm.
PRACTICE QUESTIONS
Q1 (QUANTITATIVE): A 50 kg student sits 2 meters from the pivot of a see-saw. Where must a 100 kg student sit to balance the see-saw?
Show Answer & Explanation
Answer: 1 meter from the pivot on the opposite side.
Explanation: For equilibrium, . So, meter.
Q2 (CONCEPTUAL): Why is it easier to open a heavy door by pushing at the edge furthest from the hinges?
Show Answer & Explanation
Answer: Increasing the lever arm (r) increases the torque for the same amount of force.
Explanation: Torque is the product of force and lever arm. By pushing further from the axis of rotation, you maximize the rotational effect (torque) with minimal effort (force).
Q3 (AP-FRQ): A uniform wooden plank of mass M and length L is supported by two scales, one at each end. A heavy box of mass 2M is placed at a distance L/4 from the left end. Calculate the reading on the left scale.
Show Answer & Explanation
Answer: 2Mg
Explanation: Sum torques about the right end: . Solving for : , so .
