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The speedometer of a truck is set to read the linear speed of the truck, but uses a device that actually meausres the angular speed of the rolling tires that came with the truck. However, the owner replaces the tires with larger-diameter versions. Does the reading on the speedometer after the replacement give a speed that is less than, equal to, or greater than the true linear speed of the truck?

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Answer:

Speed less than the true linear speed of the truck.

Explanation:

-Angular velocity best describes the rotational motion of a rigid body(entire object).

-In contrast, tangential velocity(only describes motion of a single point of the body),[tex]v_T[/tex] is proportional to the radius and angular velocity and is defined as:

[tex]v_T=r\omega[/tex]

-The wheels in a rolling motion and the linear sped is defined as:[tex]v=r\omega[/tex]

#As shown in the two equations,[tex]v,v_T[/tex], linear speed is directly proportional to [tex]r[/tex]. The angular displacement will however decrease  thus a lower reading on the speedometer.

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