Circular motion of a clock

In summary, the problem statement involves finding the average acceleration of a clock's minute hand as it moves from the 4 position to the 8 position, and determining the coefficient of friction required to keep a person with a mass of 55kg from slipping down on an amusement ride with a rotating cylinder of 6.6m diameter and a rotational frequency of 0.48. To solve these problems, one must use equations such as v=(4pi^2r)/(t^2) and a=v^2/r, and consider forces such as the normal force and friction force.
  • #1
lil-devil
1
0
The problem statement
a) for a clock with minute hand 20 cm long find the average accelration of the hand as it moves from the 4 position to the 8 position

b)an amusement ride is a rotating cylinder where the person is plastered to the inside wall as the ride speeds up and the floor drops away. if the cylinder is 6.6m across and turns 10.362 times in 21.5s what coeffient of friction is required to keep a person with mass 55kg from slipping down


The attempt at a solution
a)
data given
40min-->2400 secs (40 min since 4-8=40min)
20cm-->0.2m
1hour-->3600 sec

so first i drew a circle with tangents from 4 and 8 labling one tangent v1 and the other v2
and used this equation to find v
v=(4pi^2r)/(t^2) then from there on I am not sure how you get acceleration since the other formula i can think of is a=(deltaV)/(delta t)
but i can't use that formula since i don't have the differences in velocity so I am not sure where to go from that

b)
givens
6.60m diameter -->radius=3.3 (6.6/2)
freq=0.48 -->(10.362/21.5)
got a fdb

^friction
|
Fn<--o
|
v mg

so fnety=f-mg
since the guy isn't falling
fnety=0
therefore f=mg
since
f=mewFn
mg=mewfn
so there's 2 unknowns, how do you find Fn?


Thanks in advance ^^
 
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  • #2
For a), yes, delta(v)/delta(t). The speed at the two times is the same. But the velocity is different because velocity is a vector. The direction changes. For b) your notation is somewhat opaque. Find the normal force N at the given rotation speed. It has to produce a central acceleration on the person of v^2/r, right? What do you get? Then, ok, mg is the downward force and mu_static*N is the upward force. Balance them.
 
Last edited:

1. What causes the circular motion of a clock?

The circular motion of a clock is caused by the oscillation of a pendulum or the rotation of a balance wheel, which is regulated by a series of gears and springs. This motion is what drives the hands of the clock to move in a circular motion.

2. How does a clock maintain its constant circular motion?

A clock maintains its constant circular motion through the use of a power source, such as a battery or a winding mechanism, which provides energy to the gears and springs that regulate the motion of the pendulum or balance wheel. This consistent energy input ensures that the clock continues to move in a circular motion without slowing down or speeding up.

3. Can the circular motion of a clock be affected by external factors?

Yes, the circular motion of a clock can be affected by external factors such as temperature, humidity, and friction. These factors can cause the gears and springs in a clock to expand or contract, which can affect the accuracy and consistency of the circular motion.

4. How does the circular motion of a clock impact its accuracy?

The circular motion of a clock is directly related to its accuracy. If the gears and springs that regulate the motion are well-designed and maintained, the clock will have a more accurate and consistent circular motion. However, if these components are damaged or worn, it can cause the clock to lose accuracy over time.

5. What are some common problems that can occur with the circular motion of a clock?

Some common problems that can occur with the circular motion of a clock include the clock running too fast or too slow, the hands getting stuck or skipping, and the clock making a ticking noise. These problems can be caused by various factors such as worn components, improper maintenance, or external influences.

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