It didn't say that. The angle between two vectors is obtained by putting them tail-to-tail. If you do that with r and F, you will get an angle of 120°. Then note that ##rF\sin(120^{\circ})=rF\cancel{\sin}\cos(30^{\circ}).##MatinSAR said:
You probably meant to write ##rF\sin(120^{\circ})=rF\cos(30^{\circ}).##kuruman said:
Yes, of course. Good catch.Steve4Physics said:
So the book is wrong since sin30 isn't equal to sin120 degrees... @Lnewqbankuruman said:
Torque is a measure of the rotational force applied to an object. It is calculated using the formula: Torque (τ) = Force (F) x Lever Arm Distance (r) x sin(θ), where F is the force applied, r is the distance from the axis of rotation to the point where the force is applied, and θ is the angle between the force vector and the lever arm.
Torque is typically measured in Newton-meters (Nm) in the International System of Units (SI). In the Imperial system, torque can be measured in pound-feet (lb-ft).
The angle of the applied force affects the torque because torque is calculated as τ = F x r x sin(θ). If the force is applied perpendicular to the lever arm (θ = 90 degrees), sin(θ) is 1, and the torque is maximized. If the force is applied parallel to the lever arm (θ = 0 degrees), sin(θ) is 0, and the torque is zero.
The lever arm distance is the perpendicular distance from the axis of rotation to the line of action of the force. For a cylinder, this distance can be measured from the axis of the cylinder to the point where the force is applied.
The radius of the cylinder affects the lever arm distance (r) in the torque calculation. A larger radius increases the lever arm distance, which in turn increases the torque produced by a given force, assuming the force is applied at the edge of the cylinder.