TutorMe homepage

SIGN IN

Start Free Trial

Mykolas Z.

Online tutor for a year; taught undergraduates at Cambridge for four years

Tutor Satisfaction Guarantee

Physics (Newtonian Mechanics)

TutorMe

Question:

An ice skater is spinning on ice at some constant angular velocity $$\omega$$ with their arms stretched out. When they pull their arms in while still spinning, $$\omega$$ increases. Explain why.

Mykolas Z.

Answer:

We apply conservation of angular momentum: $$I_1\omega_1 = I_2\omega_2$$. By pulling their arms in, the ice skater decreases their moment of inertia $$I$$. So if $$I_2 < I_1$$ and $$I_1\omega_1 = I_2\omega_2$$, it means that $$\omega_2 > \omega_1$$: their angular velocity has increased.

Calculus

TutorMe

Question:

Integrate $$x \ln{(x)}$$.

Mykolas Z.

Answer:

We use integration by parts, which can be derived by differentiating a product of two functions: $$\int u dv = uv -\int v du$$. Applying this rule once, with $$v = \frac{x^{2}}{2}$$ and $$u = \ln{x}$$, we get: $$ \int x\ln{(x)} dx = [\frac{x^{2}}{2}\ln{(x)}] - \int{\frac{x^{2}}{2}\frac{1}{x}dx} + C_0 = [\frac{x^{2}}{2}\ln{(x)}] - \frac{x^{2}}{4} +C_1$$, where $$C_0$$ and $$C_1$$ are integration constants.

Physics

TutorMe

Question:

You have three resistors, each having a resistance of 5 Ohms. Construct a circuit that has the lowest possible resistance using all three resistors. What is that resistance? Now construct a circuit using all three resistors that has the highest possible resistance. What is it?

Mykolas Z.

Answer:

The lowest resistance would be when the resistors are all connected in parallel. The resistance then becomes: $$\frac{1}{R} = \frac{1}{5} + \frac{1}{5} + \frac{1}{5}$$; $$R = \frac{5}{3} \Omega$$. The highest resistance is achieved when all three resistors are connected in series, $$R$$ then becomes: $$R = 5 + 5 + 5 = 15 \Omega$$.

Send a message explaining your

needs and MYKOLAS will reply soon.

needs and MYKOLAS will reply soon.

Contact MYKOLAS

Ready now? Request a lesson.

Start Session

FAQs

What is a lesson?

A lesson is virtual lesson space on our platform where you and a tutor can communicate.
You'll have the option to communicate using video/audio as well as text chat.
You can also upload documents, edit papers in real time and use our cutting-edge virtual whiteboard.

How do I begin a lesson?

If the tutor is currently online, you can click the "Start Session" button above.
If they are offline, you can always send them a message to schedule a lesson.

Who are TutorMe tutors?

Many of our tutors are current college students or recent graduates of top-tier universities
like MIT, Harvard and USC.
TutorMe has thousands of top-quality tutors available to work with you.

Made in California

© 2019 TutorMe.com, Inc.