Three forces are applied to a wheel of radius 0.350 m, as shown in Fig. E10.4. One force is perpendicular to the rim, one is tangent to it, and the other one makes a 40.0° angle with the radius. What is the net torque on the wheel due to these three forces for an axis perpendicular to the wheel and passing through its center?

Verified step by step guidance

1. Identify the forces acting on the wheel: 11.9 N perpendicular to the rim, 8.50 N tangent to the rim, and 14.6 N at a 40.0° angle to the radius.
2. Recall the formula for torque: \( \tau = r \cdot F \cdot \sin(\theta) \), where \( r \) is the radius, \( F \) is the force, and \( \theta \) is the angle between the force and the lever arm.
3. Calculate the torque for the 11.9 N force: Since it is perpendicular to the radius, \( \theta = 90° \), so \( \tau_1 = 0.350 \text{ m} \cdot 11.9 \text{ N} \cdot \sin(90°) \).
4. Calculate the torque for the 8.50 N force: It is tangent to the rim, so \( \theta = 90° \), thus \( \tau_2 = 0.350 \text{ m} \cdot 8.50 \text{ N} \cdot \sin(90°) \).
5. Calculate the torque for the 14.6 N force: It makes a 40.0° angle with the radius, so \( \tau_3 = 0.350 \text{ m} \cdot 14.6 \text{ N} \cdot \sin(40.0°) \).

Key Concepts

Torque

Torque is a measure of the rotational force applied to an object, calculated as the product of the force and the lever arm distance from the axis of rotation. It is given by the formula τ = r × F × sin(θ), where r is the radius, F is the force, and θ is the angle between the force and the lever arm. Torque determines how effectively a force can rotate an object around an axis.

Lever Arm

The lever arm is the perpendicular distance from the axis of rotation to the line of action of the force. It is crucial in calculating torque because it determines the effectiveness of the force in causing rotational motion. A longer lever arm increases the torque for the same amount of force, making it easier to rotate the object.

Net Torque

Net torque is the sum of all individual torques acting on an object, taking into account their directions. It determines the overall rotational effect on the object. If the net torque is zero, the object remains in rotational equilibrium, meaning it does not start rotating or change its rotational speed. Calculating net torque involves adding torques that cause rotation in the same direction and subtracting those that oppose it.