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## Unit 1: Polynomial arithmetic

Unit 2: complex numbers, unit 3: polynomial factorization, unit 4: polynomial division, unit 5: polynomial graphs, unit 6: rational exponents and radicals, unit 7: exponential models, unit 8: logarithms, unit 9: transformations of functions, unit 10: equations, unit 11: trigonometry, unit 12: modeling.

## ME 274: Basic Mechanics II

Homework h5.c - sp24.

NOTE: The view of the figure provided is that of the rod as seen from above the surface on which the rod lies.

## 21 thoughts on “Homework H5.C - Sp24”

Does a frictionless horizontal surface mean that it is on a horizontal plane?

Correct. This means that gravity does not need to be taken into account

Is there a normal force to account for in this question?

The only normal force would be opposing gravity, coming out of the page. Since this is in the horizontal plane we do not need to account for gravity and therefore we do not need to account for the normal force. The only force in your FBD should be force F

Would kinamatics be required for this question? If F is the only force acting on the rod I believe the question can be solved just through Newton/Eulers, would this be correct?

If in any kinetics problem in this course that you find that you do not need kinematics, then simply write: "Step 3: kinematics - NOT NEEDED.

In this problem, you do not need kinematics.

This is correct. You do not need kinematics in this problem since there isn't a problem where we have too many unknowns. The inertia is of the center of mass which is 1/12mL^2 based on the chart for inertia in our lecture book. Dividing F by g will give you your mass to solve a and b. Acceleration can be found by finding the force in the x and y directions and angular acceleration can be found by finding the torques that correspond to inertia times alpha.

MOI for a uniform rod around its center is 1/12 * m * L^2.

After solving for the acceleration of G, you will need to use M = IA (where I is moment of inertia and A is angular acceleration of the rod).

The mass is given in terms of pounds, which is mass*gravity. It's important to remember to divide this value by gravity in imperial units to find the mass alone when plugging into equations

Please note that the "weight" of the bar is given in terms of pounds.

I know that we need to use the M = IA Formula. However, I am confused on when we would use the (r cross ma) term if we are using the same equation and why it crosses out here.

For different problems, the 'r cross ma' term could be 'crossed out' for different reasons. Your goal should be to choose a point A such that this term goes to zero/ is 'crossed out'. In this problem specifically, if you choose the point A as the center of mass, then the position vector from A to G becomes a zero vector , and the whole cross product term goes to zero - simplifying our math.

I think it would be helpful to reference pg. 298 in the lecture book which explains it. This problem essentially falls into the first bullet point: by choosing the point of interest to be the center of mass, then the position vector is 0 and (r cross ma)=0. You would need to use the r cross ma when the point you choose is NOT 1) center of mass 2) fixed 3) with r(G/A) parallel to acceleration vector

All of the above cases have (r cross ma)=0, and we purposely choose a point such that we do not have to calculate r cross ma

When solving this hw, I did not need to use either accelerations to solve for each other. They were separate equations from the book. Similar to lecture

What helped solve this problem more easily is to remember that the Y component of the force being applied is cancels out when taking the moment around the center of mass.

The weight of the bar and the force acting on the bar are both given in lbs, so no unit conversion is necessary such as mg --> m

When dealing with a frictionless horizontal surface, we don't need to worry about gravity or its effect on the surface. We mainly focus on the force F acting on the rod, without considering motion equations. Remembering to use the moment of inertia formula M=IA is important, especially when figuring out how the rod rotates. Choosing A to be at the same location as the center of mass G, helps simplify calculations by eliminating unnecessary terms like r×ma. This method is all about making the math easier, as explained in the lectures.

In this problem, because the rod is in the horizontal plane and there is only one force, only kinetics are required to solve

You do not need kinematics in this problem since there isn't a problem where we have too many unknowns. The inertia is of the center of mass which is 1/12mL^2 based on the chart for inertia in our lecture book. Dividing F by g will give you your mass to solve a and b. Acceleration can be found by finding the force in the x and y directions and angular acceleration can be found by finding the torques that correspond to inertia times alpha.

When doing this problem, you will notice that you do not need to create any kinematic equations, you are able to solve with just kinetics. It is still important to realize that you need to use a moment equation about the center of gravity for this to occur.

Women's Health

## 9 Best Magnesium Supplements Of 2024, According To Experts

Posted: March 31, 2024 | Last updated: March 31, 2024

## 1) Magnesium Glycinate

If you’re looking for an easily digestible magnesium supp with great all-around benefits, Baswick suggests magnesium glycinate from the brand Nature Made. It’s gentle on the stomach while scoring high in absorption to support muscle relaxation, bone health, heart health, and nerve health.

Reviewers say that the supplement has helped them relax, sleep better, and even digest food more easily. Some say that the supp itself is a bit large, so if you're not used to taking big capsules, it may take some getting used to. (Pro tip: Apart from water, a spoonful of applesauce can help!)

## 2) Magnesium Bisglycinate

If you're ready to incorporate magnesium into your wellness routine but don't love taking huge capsule pills, this is the product for you. Taking it is simple: Mix one scoop with eight ounces of water daily, per the website .

“Many of my clients struggle with swallowing pills on a daily basis. This powder form of magnesium is not only easily digested and absorbed by the body, but it can also be mixed in with water, milk, juice, or any liquid of choice to make it go down smoother,” says Moskovitz.

Add it to your favorite smoothie recipe for a nourishing boost, or mix it in with a protein shake after your next workout to help you wind down and recover. The lightly sweetened powder is also perfect for a pre-bedtime drink to purportedly help relax your muscles and support a healthy heart, brain, and lungs.

## 3) Magnesium Complex with Vitamin D and Zinc

If you prefer a supplement that targets multiple health goals, you'll appreciate this option from Nature Made. It contains vitamin D3 and zinc , both of which can help boost your immune system and support your overall wellness.

“This cocktail of essential nutrients contains a variety of types of magnesium that can target everything from digestion to blood sugar balance,” says Moskovitz. Plus, the addition of vitamin D and zinc make it beneficial for your immune system, bone health, and fighting inflammation, she adds.

Reviewers say the supplement has helped them with sleep, digestion, anxiety, and staying calm. And although it won't put you to sleep in minutes, some users claim it subtly supports relaxation with consistent use.

## 4) Magnesium Caps

These NOW magnesium caps contain multiple forms of magnesium which may help with absorption, says Baswick. One capsule also gives you the full dose (400 milligrams), so you don't have to worry about swallowing multiple large pills every time.

Many reviewers claim the capsules have helped with sleep and relaxation. Some mention that it's "easy to swallow" and doesn't give them tummy issues (a major plus). If you're new to supplements and want to avoid the pesky side effects of a new pill, this one is for you. Plus, each bottle is non-GMO certified, vegan, kosher, and keto-friendly.

## 5) Magnesium + Ashwagandha Supplement

This combination of magnesium and ashwagandha (an adaptogen that targets the body's natural stress response) can help with calming your mind and body, says Moskovitz. The formula is also easy to absorb and digest in the body, she adds.

Apart from rest and relaxation, the brand claims the supplement can support muscle recovery, bone health, and heart health—great for any athletes or folks who regularly engage in strength training (but don't want to be sore afterward). Plus, New Chapter is regulated and stamped with NSF third-party approval.

## 6) Magnesium 8

If you’re looking for a higher dosage based on your doctor’s recommendation, this supplement from AvalonX might be a good option for you. The supplements contain eight different forms of magnesium to support energy, metabolism, muscle recovery, stress, cardiovascular health, and more.

The recommended dosage is two capsules daily, or as recommended by your doctor. It can be taken anytime, with or without food. Reviewers claim the product has helped with sleep, digestion, and even headaches.

The supps are also quadruple lab tested and manufactured and regulated in a certified facility, which Moskovitz says is key when choosing the best product for you. For an added bonus, the glass packaging is sustainable, and the vegan product is free of all common allergens, including gluten, wheat, soy, dairy, nuts, eggs, shellfish, and rice.

## 7) Magnesium Gummies

If you’re looking for a tasty, chewable supplement, Baswick gives the thumbs-up to Trace Minerals magnesium gummies. The product can supposedly help with stress, relaxation, muscle recovery, and immunity, and it comes in fruity flavors like tangerine and peach.

The supplements are third-party tested and they make an easy alternative compared to powders and large pills. If you're new to supps, this gummy option can be a simple option to add to your routine. Just be mindful that the gummies do contain inulin—a prebiotic that may not be as digestible for those with stomach troubles or irritable bowel syndrome (IBS), Baswick adds.

## 8) Mega-Mag 400 mg Liquid Magnesium Chloride

If pills, capsules, and gummies aren't your thing, you can also take magnesium via dropper for easy supplementation. This option from Trace Minerals comes in a liquid form, so it’s perfect for adding to water, juice, or a smoothie, says Baswick. Each serving is also free of artificial ingredients and added sugars.

For best results, the brand recommends four to five drops in your water, juice, or coffee and taking it with a meal or a snack. You can gradually ramp up your dosage over time or dilute to your taste preference, but always consult your doctor before experimenting.

## 9) Neuro-mag Magnesium L-threonate

This form of magnesium is easily and well absorbed in the body, says Baswick. This option from Life Extension can help you maintain healthy levels of magnesium if you don't get enough from your diet.

If you're new to magnesium, the company recommends starting small with a reduced dose (one capsule daily) and slowly increasing dosage to the recommended serving size of three capsules as needed or advised by your doc.

The gluten-free and non-GMO capsules are also vegetarian and uniquely designed for memory, focus, and cognition, according to the company, which makes them a great addition to your daily routine—of course, with your doc’s approval!

## 10) What are the side effects of magnesium supplements?

Side effects are typically minimal, but if taken on an empty stomach, digestive upset, cramping, nausea, and diarrhea are possible, says Baswick. However, choosing the more well-absorbed forms of magnesium supplements may help to prevent symptoms, she adds.

## 11) Are magnesium supplements safe?

It's always best to talk with your doctor and let them advise you based on your specific needs, says Dr. Pulde. Supplements aren’t regulated by the Food and Drug Administration (FDA), so if you're purchasing over-the-counter supplements, do your homework and buy a reputable brand with ingredient transparency and third-party testing, she adds. To make it easier, Moskovitz recommends looking for a Consumer Lab, USP, or NSF seal on the supplement bottle to indicate third-party testing.

## 12) Can you take too much magnesium?

“Consuming magnesium-rich foods should never cause any problems, but it is absolutely possible to overdo it with supplement use,” says Baswick. “It’s always important to consume supplements under the tolerable upper intake limit, which in this case is 350 mg for magnesium (unless directed by a doctor), because if someone were to take an excessive amount of magnesium supplements it could cause diarrhea, nausea, or abdominal pain,” she explains. In extreme cases, magnesium toxicity can cause more severe symptoms such as muscle weakness, difficulty breathing, or cardiac arrest, she adds.

## 13) Is Epsom salt a magnesium supplement?

Epsom salt (also known as magnesium sulfate) may raise magnesium levels in the body when added to a bath, though it may be a less efficient way to increase your magnesium levels, says Dr. Pulde. In fact, according to the Cleveland Clinic , there are no definitive studies showing that magnesium can be absorbed through your skin in sufficient amounts to address deficiencies. Anecdotally, an Epsom salt bath may relieve stress , muscle pain, or inflammation.

## 14) How Our Team Chose The Best Magnesium Supplements

Women’s Health editors, including writer Andi Breitowich, researched the bestselling, most popular, and top-rated magnesium supplements. Our team consulted Jenn Baswick, RD, Lisa Moskovitz, RD, and Alona Pulde, MD, and then evaluated thousands of customer reviews and ratings to narrow down the best nine items for a wide range of needs and preferences.

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#### IMAGES

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23. 9 Best Magnesium Supplements Of 2024, According To Experts

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