When you pedal a bicycle, maximum torque is produced when the pedal sprocket arms are in the horizontal position, and no torque is produced when they are in the vertical position. Explain

This is because when the pedal sprocket arms are in the horizontal position, it is perpendicular to the applied force, and the angle between the applied force and the pedal sprocket arms is 90⁰.  

Also, when the pedal sprocket arms are in the vertical position, it is parallel to the applied force, and the angle between the applied force and the pedal sprocket arms is 0⁰.

Explanation:

τ = r×F×sinθ

where;

τ is the torque produced

r is the radius of the pedal sprocket arms

F is the applied force

θ is the angle between the applied force and the pedal sprocket arms

Maximum torque depends on the value of θ,

when the pedal sprocket arms are in the horizontal position, it is perpendicular to the applied force, and the angle between the applied force and the pedal sprocket arms is 90⁰.

τ = r×F×sin90⁰ = τ = r×F(1) = Fr (maximum value of torque)

Also, when the pedal sprocket arms are in the vertical position, it is parallel to the applied force, and the angle between the applied force and the pedal sprocket arms is 0⁰.

τ = r×F×sin0⁰ = τ = r×F(0) = 0 (torque is zero).