The motion of the wheel of a bicycle moving on a smooth straight road is

Analyze the question: We need to describe the motion of a bicycle wheel as the bicycle moves along a smooth, straight road.

Concept: A body can show different types of motion:

• Translational motion: the whole body moves from one point to another along a path (here, a straight line).
• Rotational motion: the body spins about an axis.
• Oscillatory (vibratory) motion: a to-and-fro motion about a fixed point, like a pendulum.
• Random motion: irregular, unpredictable motion, like gas molecules or Brownian motion.

Solution:

1. The wheel spins about its axle, so it has rotational motion.
2. The axle and the whole wheel move forward along the straight road, so it has translational motion.
3. The road is smooth and straight, so there is no bumping up and down (no oscillation), and the movement is orderly, not random.

So the wheel combines rotation about its axle with translation along the road. This is the same as rolling motion.

Options A, B, C and D each include "oscillatory" or "random", which do not apply here. Only E has the two correct types of motion.

Answer: E. rotational and translational

Exam tip: When you see a rolling object (wheel, ball, cylinder), think "rotation + translation". Words like "smooth" and "straight" in the question are clues that rule out oscillatory and random motion.