Chapter 6: Uniform Circular Motion and Gravitation

Question 1

Define angular velocity

Answer 1

the rate of change of the angle with which an object moves on a circular path

Symbol: ω

Question 2

Define arc length

Answer 2

Δs, the distance traveled by an object along a circular path

Question 2

Define banked curve

Answer 2

the curve in a road that is sloping in a manner that helps a vehicle negotiate the curve

Question 3

Define center of mass (com)

Answer 3

the point where the entire mass of an object or of a system of objects can be thought to be concentrated

Question 4

Define centrifugal force

Answer 4

a fictitious force that tends to throw an object off when the object is rotating in a non-inertial frame of reference

Question 5

Define centripetal acceleration

Answer 5

the acceleration of an object moving in a circle, directed toward the center

Question 6

Define centripetal force

Answer 6

any net force causing uniform circular motion

Question 7

Define coriolis force

Answer 7

the fictitious force causing the apparent deflection of moving objects when viewed in a rotating frame of reference

Question 8

Define fictitious force

Answer 8

a force having no physical origin

Question 9

Define gravitational constant, G

Answer 9

a proportionality factor used in the equation for Newton’s universal law of gravitation; it is a universal constant—that is, it is thought to be the same everywhere in the universe

Question 10

Define ideal angle

Answer 10

the angle at which a car can turn safely on a steep curve, which is in proportion to the ideal speed

Question 11

Define ideal banking

Answer 11

the sloping of a curve in a road, where the angle of the slope allows the vehicle to negotiate the curve at a certain speed without the aid of friction between the tires and the road; the net external force on the vehicle equals the horizontal centripetal force in the absence of friction

Question 12

Define ideal speed

Answer 12

the maximum safe speed at which a vehicle can turn on a curve without the aid of friction between the tire and the road

Question 13

Define microgravity

Answer 13

an environment in which the apparent net acceleration of a body is small compared with that produced by Earth at its surface

Question 14

define Newton’s Universal law of gravitation

Answer 14

every particle in the universe attracts every other particle with a force along a line joining them; the force is directly proportional to the product of their masses and inversely proportional to the square of the distance between them

Question 15

Define non-inertial frame of reference

Answer 15

an accelerated frame of reference

Question 16

Define radians

Answer 16

A unit of angle measurement

Question 17

Define radius of curvature

Answer 17

Radius of a circular path

Question 18

Define rotation angle in words

Answer 18

the ratio of the arc length to the radius of curvature on a circular path

Question 19

What is the rotation angle equation?

Answer 19

Δθ=Δs/r

Δθ = change in angle
Δs = change in arc length
r = radius

Question 20

Define ultracentrifuge

Answer 20

a centrifuge optimized for spinning a rotor at very high speeds

Question 21

Define uniform circular motion.

Answer 21

the motion of an object in a circular path at a constant speed

Question 22

A pilot can withstand an acceleration of up to 9g, about 88m/s^2 before blacking out. What is the acceleration experience by a pilot flying in a circle of constant radius at a constant speed of 525 m/s if the radius is 2820 m?

Answer 22

98 m/s^2 (yes the pilot blacks out)

Explanation:

I. Assess what you have: radius, and velocity

II. Asses what you need: Centripetal acceleration

III. Find a fitting equation: a_c = v^2 / r

IV: Plug in the numbers: a_c = 525m/s^2 / 2820 m

V. Solve: 98m/s^2

Question 23

What is the equation for centripetal acceleration?

Answer 23

a_c = v^2 / r

a_c = centripetal acceleration (using _ to represent subscript)
v = velocity
r= radius

Question 24

Hai swings a ball in a verticle circle as the end of a strong that always remains taut.

At the top of the circle, the centripetal force on the ball is…

A. one-half its weight
B. Twice its weight
C. smaller than its weight
D. larger than its weight
E. equal to its weight

Answer 24

D. larger than its weight

Explanation: The centripetal force is larger than the weight at the top of the circle because the weight and the tension forces both point toward the center of the circle

Question 25

Sandra is on a rotating Ferris wheel.

When Sandra is at the bottom of the Ferris wheel’s rotation, how does the magnitude of the normal force N exerted on her by her seat compare to her weight mg?

A. N = 2mg
B. N = mg
C. N < mg
D. N > mg
E. N = 1/2 mg

Answer 25

D. N > mg

Explanation: The normal force must be larger than the wight in order for there to be a centripetal force

Question 26

According to Newton’s Law of universal gravitation F = G (m1m2/r^2)

If both masses are doubled, the force is…

Answer 26

Four times as much as the original

Question 27

According to Newton’s Law of universal gravitation F = G (m1m2/r^2

If the radius is doubled, the force is…

Answer 27

One-forth of the original value