Question

How to find sin and cos of torque on a lever?

Answer 1

To calculate torque, you must determine the angle between the force and lever arm, use the torque formula T = rF sin θ, and apply the right-hand rule to determine the sign of the torque.

Step-by-step explanation:

To find the sin and cos of torque on a lever, follow these steps:

1. Choose a coordinate system with the pivot point as the origin.
2. Determine the angle (θ) between the lever arm and the force vector (F).
3. Use the equation T = rF sin θ, where T is the torque, r is the magnitude of the lever arm, and F is the magnitude of the linear force, to calculate the magnitude of the torque.
4. To determine the sign of the torque, take the cross product of the position vector (r) and the force vector (F).
5. Apply the right-hand rule to determine if the torque is positive (counter-clockwise) or negative (clockwise).

By maximizing the angle to 90 degrees (θ = 90°), the sin θ becomes 1, which leads to the maximum torque since T = rF sin θ. Use the right-hand rule for the sign, and sum all individual torques to find the net torque on the system.