Step 1: Identify the motion of the wheel
The wheel is rolling without slipping along a horizontal road from left to right.
Step 2: Determine the velocity of point M.
Since the wheel is rolling without slipping, the velocity of any point on the rim of the wheel can be found by considering both the translational and rotational motion of the wheel. Point M is at the top of the wheel, so it has both the translational velocity of the wheel and the rotational velocity due to the wheel's rotation.
Step 3: Calculate the translational and rotational velocities
- Translational velocity: This is the velocity of the center of the wheel, which is moving to the right.
- Rotational velocity: This is the velocity due to the wheel's rotation. At the top of the wheel, this velocity is also directed to the right.
Since the wheel is rolling without slipping, the magnitude of the rotational velocity at the top of the wheel is equal to the translational velocity.
Step 4: Combine the velocities
At point M, the translational and rotational velocities add up. Both velocities are directed to the right, so the total velocity at point M is:
velocity at M = Translational velocity+Rotational velocity
Step 5: Determine the initial direction of the detached particle
When the piece of mud detaches from point M, it will initially follow the direction of the velocity it had at the moment of detachment. Since both the translational and rotational velocities are to the right, the initial direction of the detached particle will be to the right.
Final answer
Therefore it follows the arrow C
