Question

If a car moves round a circular road of radius r at a constant speed v, (A) its velocity changes and the acceleration is v/r^2 (B) there is no force on the car since its speed is constant (C) there is no velocity change since the speed is constant (D) the force on the car is towards the center and is mv^2/r (E) the force on the car is outwards from the center and is v^2/r.

Answer 1

Explanations & Calculations

• Velocity is a vector quantity meaning that it has both a magnitude & a direction of action. Therefore, as the car moves instantaneous direction changes resulting a change in velocity even though the magnitude is constant.
• Due to the change in velocity there is an acceleration ($\because \frac{\Delta v}{t}=a$ ) & it's towards the center with a magnitude of $\Large\bold{\frac{v^2}{r}}$.
• According to Newton's second law a force is generated along that direction.
• That force is called the "centripetal force" & it acts (on the particle meant to be in motion) towards the center of the locus of the motion with a magnitude of (F=ma=) $\Large\bold{\frac{mv^2}{r}}$
• A sensation of outward force is fictitious relative to the passenger

Then,

• (A) partially correct
• (B) completely incorrect.
• (C) complete incorrect
• (E) completely incorrect
• Therefore, the fully correct answer is (D)