Mr. Nechleba's Physics & Math Tutoring

Many students find rotational motion difficult, as it involves concepts which we less commonly use in our everyday lives. I've found it helpful to scaffold understanding of rotational concepts upon the more familiar concepts of translational motion. Here is one such chart that I've used with my students to help them understand more deeply torque & rotational dynamics. For those preparing for the AP Physics 1 exam or the AP Physics C exam, feel free to copy this chart into your formula sheet and use it as an aid to help you remember the important concepts of both translational and rotational dynamics.

𝗣𝗥𝗢𝗕𝗟𝗘𝗠 𝗢𝗙 𝗧𝗛𝗘 𝗪𝗘𝗘𝗞!

Galileo drops a cannonball initially at rest from the mast of a ship of height H above the deck. The ship is moving relative to the shore with a horizontal velocity of v.
a) From the reference frame of the moving ship, determine the x and y coordinates as a function of time of the cannonball from when the cannonball is released to the time the cannonball hits the deck below. Describe in everyday language the trajectory of the cannonball Galileo and the sailors on deck would see.
b) From the reference frame of someone on shore, determine the x and y coordinates of the cannonball as a function of time from when the cannonball is released to the time the cannonball hits the deck. Describe in everyday language the trajectory of the cannonball that the onlookers on shore would observe.
c) When Galileo returns to shore, he compares his trajectory of the cannonball to the people on shore. Will they agree with each other’s description of the cannonball's motion ? Why or why not ?

𝗔𝗣 𝗣𝗵𝘆𝘀𝗶𝗰𝘀 𝟭 𝗘𝘅𝗮𝗺 𝗢𝗻𝗹𝗶𝗻𝗲 𝗣𝗿𝗲𝗽 𝗦𝗲𝘀𝘀𝗶𝗼𝗻𝘀:

It's that time of the year again...AP exam prep ! In order to help my students prepare for the upcoming AP Physics 1 exam, I'm offering a series of Zoom, seminar-style group sessions going over each topic that will appear on the AP Physics 1 exam.

The series includes eight 2-hour online sessions, each covering a core AP Physics 1 unit, followed by a full-length mock exam and a final exam strategy session.

Students can enroll in the full series or attend individual units, according to the schedule below:

📅 𝗦𝗰𝗵𝗲𝗱𝘂𝗹𝗲 (𝗔𝗹𝗹 𝘀𝗲𝘀𝘀𝗶𝗼𝗻𝘀 𝗮𝗿𝗲 𝗳𝗿𝗼𝗺 𝟯𝗽𝗺-𝟱𝗽𝗺 𝗘𝗦𝗧)

• March 8 – Unit 1: Kinematics

• March 15 – Unit 2: Forces

• March 22 – Unit 3: Work, Energy & Power

• March 29 – Unit 4: Linear Momentum

• April 5 – Unit 5: Torque & Rotational Dynamics

• April 12 – Unit 6: Energy & Momentum of Rotating Systems

• April 19 – Unit 7: Oscillations

• April 26 – Unit 8: Fluids

• May 2 – Full-Length Mock Exam

• May 3 – Final Review & Exam Strategy

Write me a message for more details and sign-up !

𝗣𝗥𝗢𝗕𝗟𝗘𝗠 𝗢𝗙 𝗧𝗛𝗘 𝗪𝗘𝗘𝗞!

Let's estimate the core temperature of the sun, T. We know that the heat generated by the sun is fueled by nuclear fusion: two protons colliding and releasing large amounts of energy due to the equivalence of mass and energy. To simplify this, let's assume two protons colliding in a one-dimensional collision.

a) Ignoring quantum effects, how far apart are the centers of the protons when they collide if we treat the protons as billiard balls ? (Hint: the radius of a proton is 0.84 femtometers)

b) At this distance, how much electrical potential energy is stored here?

c) Given that this is a one-dimensional collision and using the equipartition theorem and the conservation of energy, determine the temperature of the protons necessary for the collision.

𝗣𝗥𝗢𝗕𝗟𝗘𝗠 𝗢𝗙 𝗧𝗛𝗘 𝗪𝗘𝗘𝗞!

A traditional watermill consists of a wheel of radius 𝘙 with flat paddles mounted around its rim. Water from a reservoir of height 𝘩 above the ground flows through a narrow nozzle of area 𝘈 ( 𝘩 >> √A ) and horizontally strikes the paddles of the windmill, causing the wheel to rotate about a fixed, frictionless axle. The wheel has a moment of inertia 𝘐. Express all answers in terms of the given variables or any other fundamental constants.

Assume:
•ideal fluid flow
•ignore air resistance and gravitational effects for the stream of water after it exits the nozzle.
•all of the water exiting the nozzle horizontally strikes the paddle and immediately comes to rest.

a) Determine the velocity 𝘷 of the water as it exits the nozzle

b) Determine the mass rate of flow 𝘳 for the water striking the paddle

c) Using your answer to the previous question, determine the force 𝘍 exerted on the paddle. (Hint: think in terms of momentum)

d) Now derive an expression for the torque acting on the windmill from the water.

e) In terms of the moment of inertia 𝘐 of the windmill, what is the angular acceleration of the windmill immediately after the water strikes the paddle ?

𝗣𝗥𝗢𝗕𝗟𝗘𝗠 𝗢𝗙 𝗧𝗛𝗘 𝗪𝗘𝗘𝗞!

Assume that the orbit of Earth around the Sun of mass 𝘔 is a circle of radius 𝘙.
a)Show that the square of Earth's orbital period 𝘛 is proportional to the cube of the radius 𝘙. This is Kepler's Third Law of Planetary Motion and is known as the "law of harmonies".
b)Calculate the period of Earth's orbit in terms of 𝘔, 𝘙, and other fundamental constants.
c)Now plug in the accepted values for 𝘔 and 𝘙 and obtain a numerical answer for 𝘛. Determine the percent error of your calculated value with the accepted value.

𝗣𝗥𝗢𝗕𝗟𝗘𝗠 𝗢𝗙 𝗧𝗛𝗘 𝗪𝗘𝗘𝗞!

A particle starts from rest at the top of a frictionless sphere of radius R and slides on the sphere under the force of gravity. How far below its starting point does it get before flying off the sphere? Express your answer in terms of R in the comments below !

Mr. Jeffrey Nechleba Welcome to my scheduling page. Please follow the instructions to add an event to my calendar.

❓ 𝗛𝗮𝘃𝗲 𝗔 𝗣𝗵𝘆𝘀𝗶𝗰𝘀 𝗼𝗿 𝗠𝗮𝘁𝗵 𝗤𝘂𝗲𝘀𝘁𝗶𝗼𝗻 ?

Feel free to drop it 𝗿𝗶𝗴𝗵𝘁 𝗵𝗲𝗿𝗲 𝗶𝗻 𝘁𝗵𝗲 𝗰𝗼𝗺𝗺𝗲𝗻𝘁𝘀 — I’m happy to help out!
Whether you’re studying:
• AP Physics 1 & 2
• AP Physics C (Mech / E&M)
• Algebra, Geometry, Precalculus
• Calculus
• College Physics 1 & 2
• MCAT Physics

📚 𝗢𝗡𝗟𝗜𝗡𝗘 𝗣𝗛𝗬𝗦𝗜𝗖𝗦 & 𝗠𝗔𝗧𝗛 𝗧𝗨𝗧𝗢𝗥

Hi everyone! I’m Jeff, a physics and math tutor with a B.S. in Physics and 500+ hours helping high school & college students master science and math with clarity and confidence.

All tutoring is 100% online, so you can work with me from anywhere. Sessions are calm, structured, and focused on real understanding — not memorization.

🧪 𝗦𝘂𝗯𝗷𝗲𝗰𝘁𝘀 𝗜 𝗧𝘂𝘁𝗼𝗿

AP Physics 1 & 2 (concepts, problem-solving, FRQs)

AP Physics C: Mechanics & E&M

College Physics 1 & 2 (life sciences or calc-based)

Algebra, Geometry, Precalculus, Calculus

MCAT Physics & Critical Thinking

💵 𝗣𝗿𝗶𝗰𝗶𝗻𝗴

High school students: $45/hr

AP & College courses: $55/hr

MCAT Physics: $70/hr

𝘚𝘭𝘪𝘥𝘪𝘯𝘨 𝘴𝘤𝘢𝘭𝘦 𝘢𝘷𝘢𝘪𝘭𝘢𝘣𝘭𝘦 𝘪𝘧 𝘯𝘦𝘦𝘥𝘦𝘥 — message me.

💬 𝗛𝗮𝘃𝗲 𝗾𝘂𝗲𝘀𝘁𝗶𝗼𝗻𝘀?

Message me right here on Facebook — I'm happy to talk through your goals and help you figure out the best plan.

⭐ 𝗥𝗲𝘃𝗶𝗲𝘄𝘀 𝗮𝗻𝗱 𝗧𝗲𝘀𝘁𝗶𝗺𝗼𝗻𝗶𝗮𝗹𝘀
See my 5-star ratings and student testimonials on Wyzant:
https://www.wyzant.com/Tutors/PA/Pittsburgh/9891852

📅 𝗥𝗲𝗮𝗱𝘆 𝘁𝗼 𝗯𝗼𝗼𝗸 𝗮 𝘀𝗲𝘀𝘀𝗶𝗼𝗻?
Schedule directly through my online calendar:
👉https://calendly.com/jeffnechleba

📧 𝗣𝗿𝗲𝗳𝗲𝗿 𝗲𝗺𝗮𝗶𝗹?

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