Refer to the following information for the next six questions.
A coin of mass 25 grams is placed 20 cm from the center on a rotating turntable. The coin does not slip
while the platform rotates at a constant angular speed of 40 rpm.
1. What is the magnitude of the coin's linear velocity in m/sec?
0.84
0.838 m/sec
40 rpm = 4.19 rad/sec
Now use the formula v = rω giving you v = (0.20)(4.19) = 0.838 m/sec
Another method would be to use v = 2πrf. Remember that f must be measured in rev/sec (hz)
not rev/min. This formula is equivalent to v = rω since ω = 2πf.
v = 2πrf
v = 2π(0.20)(40/60)
v = 0.838 m/sec
2. Which of the following answer correctly illustrates the direction of the coin's linear velocity at the instant
it is at the position shown in the diagram above?
3. What would be the magnitude of the acceleration experienced by the coin?
3.5
3.51 m/sec2
ac = v2/r = (rω)2/r = ω2r
ac = (4.19)2(0.20) = 3.51 m/sec2
4. Which of the following answer correctly illustrates the direction of the coin's acceleration at the instant it
is at the position shown in the diagram above?
5.
If the coefficient of static friction between the coin and the surface is 0.65, what would the greatest
rotational speed the turntable could acquire and still have the coin stay in place?
0.09
5.65 rad/sec = 53.9 rpm
6. If the first coin were to be replaced with a larger coin made of the same material, which of the following
statements is true?
the larger coin will fly off at a tangent
the larger coin will remain at rest as well
the larger coin will fly off along the radius
the larger coin will spiral in towards the center of the turntable
Refer to the following information for the next five questions.
You have completed a lab using a conical pendulum whose length was 75 cm.
During the lab you collected the following data:
mass of whirled rubber ball = 25 grams
40-second trial #1: 50 rev
40-second trial #2: 52 rev
40-second trial #3: 51 rev
mass of suspended washers = 60 grams
7. A freebody diagram of the rubber ball will show what two forces acting on the ball?
tension and weight
Note: θ is measured from the vertical
T cos θ = mg
T sin θ = Fc = mv2/r
gravity and ten
8. During the experiment, the suspended washers supplied the tension. Using the fact that mg = T cos θ,
at what angle was the ball being twirled?
33 degrees
65.4º
(0.060)(9.81) cos θ = (0.015)(9.81)
cos θ = 0.25
θ = 65.4º
9. What was the average frequency for your trials?
51 Hz
1.275 hz
f = 51 rev/40 sec = 1.275 hz
10. Using the fact that the actual twirling radius was r = L sin θ, what was the magnitude of the rubber
ball's average velocity during your trials?
4.3
5.46 m/sec
v = 2πrf = 2(π)(0.75 sin 65.4º)(1.275) = 5.46 m/sec
11. If another series of trials, with the same rubber ball and washers, had been performed but with a
shorter radius would you anticipate the tangential velocity of the ball would increase or
decease?
decrease
decrease
Since Fc remains constant (the weight of the washers), then for the same mass ball (m)
twirling at a smaller radius would demand a smaller velocity so that the ratio of F c =
mv2/r would remain constant.
12. A girl attaches a rock to a string, which she then swings counter-clockwise in a
horizontal circle. The string breaks at point P in Figure 7-4, which shows a bird's-eye
view (i.e., as seen from above). Which path (A-E) will the rock follow?
B