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ON RAMPS Physics > Rotational Motion and Gravity > Flashcards

Rotational Motion and Gravity Flashcards

These note cards deal with the simplest form of curved motion, uniform circular motion, motion in a circular path at constant speed.

1
Q

The arc length is represented with what variable in the diagram?

A

Δs

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2
Q

The rotation angle is represented with what variable in the diagram?

A

Δθ

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3
Q

The radius of curvature is represented with what variable in the diagram?

A

r

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4
Q

2 π rad = ?

A

1 revolution

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5
Q

What is the equivalent radian measure at 30°?

A
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6
Q

What is the equivalent radian measure at 60°?

A
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7
Q

What is the equivalent radian measure at 90°?

A
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8
Q

What is the equivalent radian measure at 120°?

A
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9
Q

What is the equivalent radian measure at 135°?

A
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10
Q

What is the equivalent radian measure at 180°?

A
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11
Q

How do we define angular velocity?

A

(ω) the rate of change of an angle

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12
Q

How do we define linear velocity?

A

(v) the rate of change for arc length over time.

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13
Q

How is the linear velocity related to the radius of curvature?

A

the linear velocity v is proportional to the distance from the center of rotation, thus, it is largest for a point on the rim (largest r),

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14
Q

How is angular velocity related to linear velocity?

A

directly proportional because the faster an object in a circle spins — large v means a large ω.

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15
Q

Calculate the angular velocity of a 0.450 m radius car tire when the car travels at 30.0m/s

A

30.0 m/s ÷ 0.450 m = 67 rad/s

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16
Q

The fly is currently on the outerpart of the record (r1) , if it had landed closer to the center (r2), reducing the radius or curvature. Assuming the same angular velocity, what would the new linear velocity be for the insect at r2? (LESS, MORE, EQUAL) to r1

The linear velocity at r2 will be (LESS THAN, MORE THAN, EQUAL TO) it was at r1.

A

The linear velocity at r2 will be LESS THAN it was at r1.

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17
Q

What is the definition of centripetal acceleration(ac)?

A

Centripetal acceleration(ac) is the acceleration of an object moving in uniform circular motion.

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18
Q

v1 represents the (angular, linear) velocity at point (A, B, C).

A

v1 represents the linear velocity at point B.

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19
Q

v2 represents the (angular, linear) velocity at point (A, B, C).

A

v2represents the linear velocity at point C.

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20
Q

Which equation would you use to calculate the centripetal acceleration (ac), if you are given angular velocity and radius of curvature?

A
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21
Q

Which equation would you use to calculate the centripetal acceleration (ac), if you are given linear velocity and radius of curvature?

A
22
Q

What is a centrifuge?

A

A centrifuge is a rotating device used to separate specimens of different densities.

23
Q

What is the magnitude of the centripetal acceleration of a car following a curve of radius 300 m at a speed of 40.0 m/s? Compare the acceleration with that due to gravity for this fairly gentle curve taken at highway speed.

A

(40.0 m/s)2 ÷ (300m) = 5.3 m/s2

g=9.8 m/s2

(5.3 m/s2) ÷ (9.8 m/s2) = 0.54 (about half g)

24
Q

If the radius of curvature was increased for the car in the picture and the velocity of the car was kept the same, the new centripetal acceleration would be (smaller, larger, the same) in comparison to the original centripetal acceleration.

A

The new centripetal acceleration would be smaller in comparison to the original centripetal acceleration.

25
Q

For the centrifuge in the diagram, you double the angular velocity. How much larger will the centripetal acceleration be?

A

4 times bigger than the original ac.

26
Q

Calculate the centripetal acceleration of a point 8.0 cm from the axis of an ultracentrifuge spinning at 7.8 × 104rev/min. Determine the ratio of this acceleration to that due to gravity.

A

ω = 7.8x104rev/min x 2π rad/rev x 1/60 min/sec = 8168 rad/s

ac= (0.08m)x(8168rad/s)2= 5.34x106 m/s2

g=9.8m/s2

5.34x106 m/s2 ÷ 9.8m/s2 = 5.51x105 times bigger than g

27
Q

What is the definition of centripteal force (Fc)?

A

Centripetal force (Fc) is the net force causing uniform circular motion.

28
Q

What equation can we use to find centripetal force, if we know the angular velocity?

A
29
Q

What equation can we use to find centripetal force, if we know the linear velocity?

A
30
Q

Assume that you keep the linear velocity the same for an object but reduce the radius in which an object is traveling, as seen in the diagram.

This will cause the centripetal force to (increase, decrease, stay the same).

A

This will cause the centripetal force to increase.

31
Q

What Coefficient of Friction Do Car Tires Need on a Flat Curve?

(a) Calculate the centripetal force exerted on a 900 kg car that negotiates a 500 m radius curve at 25.0 m/s.
(b) Assuming an unbanked curve, find the minimum static coefficient of friction, between the tires and the road, static friction being the reason that keeps the car from slipping

A

(a) Fc=[900kg x (25.0m/s)2] ÷ 500m = 1125N
(b) Assuming an unbanked curve, the static friction force would equal the centripetal force.

Fc = f = μsN = μsmg SOLVE FOR μs = v2/rg

(25 m/s)2 ÷ (500m x 9.80m/s2) = 0.13

32
Q

For the car in the diagram, if the minimum force of static friction is exceeded explain what would happen to the car?

A

The centripetal force required to stay in that radius of curvature for the turn would be insufficient and the car would slide off the road.

33
Q

In the following diagram what is the centripetal force equal to?

A
  • *Nsinθ**
  • normal force x sinθ*
34
Q

What equation is used to find the the ideal speed to take to take a steeply banked tight curve? (no friction).

A

v = (rgtanθ)1/2

35
Q

Calculate the speed at which a 200 m radius curve banked at 60.0° should be driven if the road is frictionless.

A

v = (rgtanθ)1/2 = (200×9.8m/s2×tan60)1/2 = 25 m/s

36
Q

Translate the following linear equation into a rotational equation.

v = v0 + at

A

𝜔 = 𝜔0 + ∝t

37
Q

Translate the following rotational equation into a linear equation.

∆θ = 𝜔0t + ½ ∝t2

A

x = v0t + ½at2

38
Q

A car accelerates uniformly from rest and reaches a speed of 20.9 m/s in 13.4 s. The diameter of a tire is 72.7 cm. Find the number of revolutions the tire makes during this motion, assuming no slipping.

A

v = v0 + at

20.9m/s = 0m/s + a(13.4s)

a = 1.55970149254 (PLUG THIS IN TO FIND DISTANCE)

x = v0t + ½at

x = ½ (1.55970149254m/s2) (13.4s)2

s = x = 140.03m (DIVIDE THIS DISTANCE BY THE CIRCUMFERENCE TO GET REVOLUTIONS)

1revolution = 2πr (USE HALF THE DIAMTER HERE FOR RADIUS)

(140.03m) x 1rev / 2π.3635m = 61.3108 revolutions

39
Q

Gravitational Force is (attractive, repulsive, both).

A

Gravitational Force is attractive.

40
Q

For two particles the gravitational force between them is directly proportional to the…

A

For two particles the gravitational force between them is directly proportional to the…

product of their masses

41
Q

What does CM stand for in the figure below?

A

Center of Mass

42
Q

For the following equation, what does the G stand for?

A

G, gravitational constant

43
Q

What does the variable r stand for?

A

The radius as a straight line from the center of mass of the two objects.

44
Q

The planets orbiting the moon travel in an _________.

A

ellipse

45
Q

What is Kepler’s Second Law?

A

Each planet moves so that an imaginary line drawn from the Sun to the planet sweeps out equal areas in equal times.

46
Q

Kepler’s third law is represented by the following equation. What do T1 and T2 stand for?

A

T1 and T2 are the period (time for one orbit) of two planets.

47
Q

Given that the Moon orbits Earth each 27.3 d and that it is an average distance of 3.84×108m from the center of Earth, calculate the period of an artificial satellite orbiting at an average altitude of 1500 km above Earth’s surface.

What variables are you given?

A

T1 , r1 , r2

48
Q

If r and T are known, what important thing can we solve for using this equation?

A

We can determine the mass of the parent body that is being orbited.

49
Q

How do we define a planet?

A

A celestial body that…

  1. is in orbit around the Sun,
  2. has sufficient mass to assume hydrostatic equilibrium and
  3. has cleared the neighborhood around its orbit.
50
Q

The driver of a car traveling at 25.4 m/s applies the brakes and undergoes a constant deceleration of 3.17 m/s2 . How many revolutions does each tire make before the car comes to a stop, assuming that the car does not skid and that the tires have radii of 0.37 m?

A

ON RAMPS Physics (2 decks)

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