- #1

EM_Guy

- 217

- 49

I'm trying to construct a free-body diagram.

The wheel has a weight and a normal force acting on it in the vertical directions. The sum of these forces must equal zero.

The wheel is rolling. So, the point at which the wheel is touching the ground has zero velocity. This is a kinematic constraint. If the wheel is rolling to the right, then the ground is exerting a static frictional force on the wheel that is directed to the left (I think). Since the wheel is rolling to the right, the wheel exerts a frictional force on the ground that is directed to the right, and by Newton's third law, the ground exerts a force on the wheel that acts to the left. Is this correct?

The motor is exerting a moment on the wheel. Since the wheel is rolling to the right, the torque would be clockwise. But I'm not sure if the moment exerted on the wheel about the center of the wheel is the same as the moment exerted on the wheel at the point at which the wheel is touching the ground.

This accounts for all the forces and moments acting on the wheel.

This is equivalent to a wheel of mass m and moment of inertia I whose center of mass has a linear acceleration to the right and the wheel has a clockwise angular acceleration. However, I'm saying that the wheel is moving at constant velocity. So both the linear and angular acceleration must be zero.

I think I'm getting screwed up on the moment exerted by the motor on the wheel. The moment about any point on the wheel is the sum of the cross products of displacement vectors and applied forces. So, the moment exerted by the motor about the center of the wheel is not the moment of the motor about the point at which the wheel is touching the ground.

I can't seem to set up sum(F) = ma and sum(M) = I*alpha equations here.