While riding a bike, a rider exerts a force of 540 N on the pedal, which when attatched to a sprocket creates a radius of rotation of 0.18 m. How much torque does the rider exert on the sprocket?
I think I have to use the formula
torque=rFsin(x)
But I'm not sure if that's right or how to solve it.
You are correct that the formula to calculate torque is given by torque = r * F * sin(x), where r is the radius of rotation, F is the force applied, and x is the angle between the applied force and the lever arm. In this case, since the force is applied tangentially to the sprocket, the angle x is 90 degrees, and sin(x) becomes 1.
To solve for the torque exerted on the sprocket, you need to substitute the given values into the formula. In this case, the force F is 540 N and the radius of rotation r is 0.18 m. Therefore, the calculation becomes:
Torque = 0.18 m * 540 N * sin(90°)
Since sin(90°) = 1, the equation simplifies to:
Torque = 0.18 m * 540 N
To find the numerical value of the torque, you can simply multiply the values:
Torque = 0.18 m * 540 N = 97.2 Nm
Therefore, the rider exerts a torque of 97.2 Nm on the sprocket.