A wheel is free to rotate about a horizontal axis through O. A force of 200N is applied at a point P2‌cm from the center O. OP makes an angle of 55∘ with x axis and the force is in the plane of the wheel making an angle of 25∘ with the horizontal axis. What is the torque?
To calculate the torque (τ) produced by a force on a wheel, the formula used is τ=rFsin‌(θ), where: r is the distance from the axis to the point of application of the force, in meters, F is the magnitude of the force, in Newtons, θ is the angle between the line of action of the force and the lever arm or radius. In this case: The distance r=2‌cm=0.02 meters (since 1‌cm=0.01m ), The magnitude of the force F=200N, The angle θ is the difference between the angle formed by OP with the horizontal ( x-axis) and the angle the force makes with the horizontal, which is 55∘−25∘=30∘. Thus, substituting these values into the torque formula: τ=0.02×200×sin‌(30∘) Since sin‌(30∘)=0.5, τ=0.02×200×0.5=2Nm Therefore, the torque produced by the force on the wheel is 2 Newton-meters, which corresponds to Option C (2 N m).