Rotational motion of a washing machine

In summary, the conversation is about two different rotational motion problems that the speaker needs help with. The first problem involves a washing machine going into the "spin cycle" and the calculations for its angular acceleration and revolutions. The second problem involves two masses connected by an arm and a pulley system, with calculations for torque and tangential speed. The expert summarizer provided a step-by-step summary of the calculations for both problems and thanked the expert for their help.
  • #1
tucky
30
0
Hi everyone….well I have just started to learn about rotational motion, therefore, I am really confused so I have two different problems that I need help on.

1.) Q: A washing machine goes into the “spin cycle”. From rest the washer starts rotating, gaining 1 rev/sec of rotational velocity each second. How long before it is spinning at 300 RPM? What it its angular acceleration? How many revolutions does it go through in getting up to 300 RPM?

When the spin cycle ends the washer comes to rest from 300 RPM in 4 seconds. What it its angular acceleration? How many revolutions does it go through?

A: I think this is totally wrong but here it is:
300rev/1min * 1min/60sec = 5 rev/sec, so would that be 5 sec?
alpha = change omega/ time
omega = 5 rev/ 1sec * 2pi = 31.4rad/sec
(31.4-0)/5 = 6.26rads, which is not even in the right units, so I know it is wrong. I don’t even know how to broach this problem?

2.) Q:Two 5 kg masses are connected by an arm that measures 5 ft from end to end. In the middle of the arm is a low-friction pivot point. A lightweight pulley 2 ft in diameter is mounted at the pivot point, with a cord wrapped around the pulley. The cord is pulled with a steady 20 N tension.

How long before the masses achieve a tangential speed of 40 mph?

A: torque = m * r^2 * alpha
20kgm/s^2 = 10kg * 1.83^2 * alpha
alpha = .597m/s^2

40mph = 17.88m/s
acceleration = change speed/ time
.597m/s^2=(17.88m/s-0m/s)/t = 30.8s
 
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  • #2
For #1 you should have quit while you were ahead. I agree with 5 s.
If you want to do it in radians, well, 1 rev. = 2Π rad. so
acceleration of 1 rev./s2 = 2Π rad./s2
300 rev./min = 5 rev./s = 10Π rad./s
so we have (10Π rad./s)/(2Π rad./s2) = 5 s.

For the next one, I don't know what your 1.83 represents, but let's try it this way:

First, the moment of inertia is ∑(m*r) and in this case r=2.5 ft. =.762 m. so
I = 10*.7622 kg*m2
For the torque, the moment arm r=2 ft.=.6096m so
T=20*.6096 N*m
Next, T= Iα so
α = I/T = (20*.6096)/(10*.7622)

You want 40 mi/hr tangential but you have to convert that into a radial velocity ω to relate it to the radial acceleration α. ω=v/r so you need
40 mi/hr * 1609 m/mi / 3600 s/hr / .6096 m (the radius) = 29.33 rad./s

Now, you can relate angular acceleration to angular velocity using
ωf = ωi + α*t (Looks familiar?)
Of course, in this case, ωi=0.

You finish it. (I get 14 sec.; hopefully I didn't screw up someplace.)
 
  • #3
thank you for your help gnome
 

What is rotational motion of a washing machine?

Rotational motion of a washing machine refers to the movement of the drum or basket in a circular motion during a wash cycle. This motion helps to agitate the clothes and clean them effectively.

How does rotational motion affect the washing machine?

Rotational motion is essential for the washing machine to function properly. It helps to mix the detergent and water with the clothes, remove dirt and stains, and rinse them effectively.

What causes the washing machine to rotate?

The rotation of the washing machine is caused by a motor that powers the drum or basket. This motor is connected to a pulley and belt system that creates the circular motion.

What is the direction of rotation in a washing machine?

The direction of rotation in a washing machine depends on the design and model. Some machines rotate clockwise, while others rotate counterclockwise. However, the direction of rotation does not affect the cleaning performance.

Can rotational motion cause damage to the washing machine?

In some cases, excessive rotational motion can cause damage to the washing machine. This can happen if the load is unbalanced or if there are heavy items, such as shoes or bricks, in the machine. It is important to follow the recommended load capacity and distribute the clothes evenly to prevent damage.

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