The wheel of a car has a radius of 0.390 m. The engine of the car applies a torque of 466 N·m to this wheel, which does not slip against the road surface. Since the wheel does not slip, the road must be applying a force of static friction to the wheel that produces a countertorque. Moreover, the car has a constant velocity, so this countertorque balances the applied torque. What is the magnitude of the static frictional force?

466-fricton*radius=momentinertia*acceleration

but acceleration is zero, so
466=friction*radius.

To find the magnitude of the static frictional force, we can use the relationship between torque and force. The torque applied by the engine is given as 466 N·m.

The torque can also be expressed as the product of the force and the distance from the point of application of the force (radius of the wheel). Mathematically, we can write:

Torque = Force x Radius

Rearranging the equation, we can solve for the force:

Force = Torque / Radius

Substituting the given values, we have:

Force = 466 N·m / 0.390 m

Calculating this expression, we find:

Force ≈ 1194.87 N

Therefore, the magnitude of the static frictional force applied by the road is approximately 1194.87 N.

To find the magnitude of the static frictional force, we can use the relationship between torque and the force of static friction. The torque applied to the wheel is equal to the product of the force perpendicular to the radius and the radius itself:

Torque = Force * Radius

In this case, the torque applied to the wheel is 466 N·m, and the radius of the wheel is 0.390 m.

Thus, we have:

466 N·m = Force * 0.390 m

To find the force, we need to rearrange the equation:

Force = Torque / Radius

Substituting the known values:

Force = 466 N·m / 0.390 m

Now we can calculate the force:

Force = 1194.87 N

Therefore, the magnitude of the static frictional force is approximately 1194.87 N.