AP Physics C: Mechanics:: Gravitation

What is UNIFORM CIRCULAR MOTION, and what is the object's SPEED (as opposed to velocity) doing throughout this type of motion?

- **A)** This concept has no actual relationship to an object's speed remaining constant while moving along a circular path
- **B)** In uniform circular motion, both speed AND velocity remain perfectly constant throughout the entire motion
- **C)** Uniform circular motion refers to an object's speed continuously CHANGING while moving in a circle, rather than remaining constant
- **D)** Motion in a CIRCULAR path at a CONSTANT SPEED -- even though speed remains constant, the object's VELOCITY (which includes direction) is continuously changing, since direction is always changing

What is CENTRIPETAL ACCELERATION, and in what DIRECTION does it always point for an object moving in a circular path?

- **A)** Centripetal acceleration always points AWAY from the center of the circular path (outward), rather than toward it
- **B)** The acceleration responsible for continuously changing an object's DIRECTION during circular motion; it always points TOWARD the CENTER of the circular path
- **C)** This concept has no actual relationship to a specific direction for the acceleration of an object in circular motion
- **D)** Centripetal acceleration always points TANGENT to the circular path, rather than toward the center

What is the mathematical FORMULA for CENTRIPETAL ACCELERATION (a_c), in terms of an object's SPEED (v) and the RADIUS (r) of its circular path?

- **A)** This concept has no actual mathematical relationship between centripetal acceleration, speed, and radius
- **B)** a_c = v / r^2 (speed divided by radius squared), rather than v-squared divided by radius
- **C)** a_c = v^2 / r -- centripetal acceleration is proportional to the SQUARE of speed, and INVERSELY proportional to the radius of the circular path
- **D)** Centripetal acceleration is INVERSELY proportional to the square of speed, rather than directly proportional to it

According to the a_c = v^2/r formula, if an object's SPEED is DOUBLED while the RADIUS of its circular path stays the SAME, how does its CENTRIPETAL ACCELERATION change?

- **A)** Speed has no actual relationship to centripetal acceleration for a circular path of constant radius
- **B)** Centripetal acceleration simply DOUBLES, treating the relationship as if it were linear rather than squared
- **C)** Centripetal acceleration is CUT IN HALF when speed doubles, the reverse of the actual relationship
- **D)** Centripetal acceleration QUADRUPLES (increases by a factor of 4), since acceleration depends on the SQUARE of speed -- doubling speed means squaring a doubled value, which is 4 times the original

According to the a_c = v^2/r formula, if the RADIUS of an object's circular path is DOUBLED while its SPEED stays the SAME, how does its CENTRIPETAL ACCELERATION change?

- **A)** Centripetal acceleration is CUT IN HALF, since acceleration is INVERSELY proportional to radius (for a constant speed)
- **B)** Centripetal acceleration QUADRUPLES when radius doubles, treating the relationship as if radius were also squared
- **C)** Radius has no actual relationship to centripetal acceleration for an object moving at a constant speed
- **D)** Centripetal acceleration DOUBLES along with the radius, the reverse of the actual inverse relationship between radius and centripetal acceleration

What is CENTRIPETAL FORCE, and is it a SEPARATE, NEW type of force, or simply a DESCRIPTIVE NAME for whichever force(s) already present happen to provide the necessary center-pointing force?

- **A)** This concept has no actual relationship to identifying which existing forces provide the necessary center-pointing force for circular motion
- **B)** Centripetal force is a completely SEPARATE, distinct type of force, unrelated to tension, gravity, friction, or normal force
- **C)** Centripetal force is NOT a separate, distinct type of force -- it is simply a DESCRIPTIVE NAME for whichever ALREADY-EXISTING force (like tension, gravity, friction, or normal force) actually provides the net center-pointing force needed to maintain circular motion
- **D)** Centripetal force is always provided EXCLUSIVELY by gravity, regardless of what is actually causing an object's circular motion

For a ball being swung in a HORIZONTAL circle on a string, what SPECIFIC force provides the CENTRIPETAL force needed to keep the ball moving in its circular path?

- **A)** The centripetal force in this scenario is provided by a separate, additional force beyond the string's tension and gravity
- **B)** GRAVITY alone provides the centripetal force for a ball swung horizontally, with the string's tension playing no actual role
- **C)** The TENSION in the string provides the centripetal force, pulling the ball toward the CENTER of its circular path
- **D)** This scenario has no actual relationship to identifying which specific force provides the centripetal force for a ball swung on a string

For a CAR driving around a FLAT (unbanked) circular curve, what SPECIFIC force provides the CENTRIPETAL force needed to keep the car moving along the curved path?

- **A)** GRAVITY alone provides the centripetal force for a car on a flat curve, with friction playing no actual role
- **B)** This scenario has no actual relationship to identifying which specific force provides the centripetal force for a car on a flat curve
- **C)** STATIC FRICTION between the tires and the road provides the centripetal force, pointing toward the CENTER of the curve
- **D)** The car's ENGINE directly provides the centripetal force, with friction playing no actual role in maintaining the circular path