The difference between the linear velocities is 3 m/s.

To find the linear velocities of a point on the rim and a point 200 mm from the axis of rotation, we need to use the relationship between linear velocity ( $v$ ) and angular velocity ( $\omega$ ):

$$v = r \cdot \omega$$

where:

• $v$ is the linear velocity,
• $r$ is the radius at which the point is located,
• $\omega$ is the angular velocity.

Step 1: Calculate the linear velocity at the rim

Given:

• Diameter of the wheel = 1 meter, so the radius $r_1$ = 0.5 meters (since radius is half the diameter),
• Angular velocity $\omega$ = 10 rad/sec.

The linear velocity at the rim ($ v_1 $) is:
$$v_1 = r_1 \cdot \omega = 0.5 \, \text{m} \cdot 10 \, \text{rad/sec} = 5 \, \text{m/s}$$

Step 2: Calculate the linear velocity of a point 200 mm (0.2 meters) from the axis of rotation

Given:

• Distance from the axis $r_2$ = 0.2 meters.

The linear velocity at this point ($ v_2 $) is:
$$v_2 = r_2 \cdot \omega = 0.2 \, \text{m} \cdot 10 \, \text{rad/sec} = 2 \, \text{m/s}$$

Step 3: Calculate the difference between the velocities

The difference between the linear velocities is:
$$\Delta v = v_1 - v_2 = 5 \, \text{m/s} - 2 \, \text{m/s} = 3 \, \text{m/s}$$

Therefore, the difference between the linear velocity of a point on the rim and that of a point 200 mm from the axis of rotation is $3 \, \text{m/s}$.