Question

Find the net torque on the wheel below about the axle through O perpendicular to the page, taking a = 5.00 cm and b = 19.0 cm. (Indicate the direction with the sign of your answer. Assume that the positive direction is counterclockwise.)

Answer 1

The net torque on a wheel, considering perpendicular forces, is calculated by the product of force, lever arm distance, and the sine of the angle between them. Angular acceleration is found using the equation τ = Ia. When frictional force is considered, it must be subtracted from the total torque before calculating angular acceleration.

Step-by-step explanation:

To calculate the net torque about the axle through O, we must take into account the forces and distances from the axle at which they act. Torque (τ) is calculated as the product of the force (F) applied, the distance (r) from the pivot point (which in this case is the axle at O), and the sine of the angle (θ) between the force vector and the lever arm vector (τ = rF sin θ). Given that the forces are acting perpendicular to the lever arm, the angle is 90 degrees, and so sin θ is 1.

To solve for angular acceleration (a), we use the equation τ = Ia, which is the rotational equivalent of Newton's second law. Here, τ is the net torque, I is the moment of inertia, and a is the angular acceleration. The moment of inertia depends on the mass distribution of the object around the axis of rotation.

When calculating the angular acceleration with opposing frictional force present, we must first calculate the torque caused by this frictional force (again through the product of force, distance, and the sine of the angle between them, which remains 90 degrees), and subtract it from the total torque applied to the wheel. We then use the adjusted net torque to find the angular acceleration using the modified τ = Ia equation.