Question

In: Physics

By making the following substitutions x becomes θ v becomes ω a becomes α F becomes...

By making the following substitutions

  • x becomes θ
  • v becomes ω
  • a becomes α
  • F becomes τ
  • m becomes I

we get a whole new physics that tells how rotating objects behave. Everything we have done all semester flips over to explain rotational physics

1. The moment of inertia is the quantity that replaces mass in all the old formulas. Not only is the mass of an object important, but also how that mass is distributed.

Find the moment of inertia of a 4 meter long stick with a mass of 23 kg, if it is spun about the center of the stick

ISphere = 2/5 MR2

ICylinder = 1/2 MR2

IRing = MR2

IStick thru center = 1/12 ML2

IStick thru end = 1/3 ML2

2. An ice skater with a moment of inertia of 10 kg m2spinning at 14 rad/s extends her arms, thereby changing her moment of inertia to 26 kg m2. Find the new angular velocity.

Hint: conserve angular momentum!

3. Find the rotational kinetic energy of a spinning (not rolling) bowling ball that has a mass of 10 kg and a radius of 0.17 m moving at 12 m/s.

(Fun fact: How can this problem be done if r isn't given?)

v = rω

ISphere = 2/5 MR2

ICylinder = 1/2 MR2

IRing = MR2

IStick thru center = 1/12 ML2

IStick thru end = 1/3 ML^2


Recall: when rolling, the ball is both moving forward and rotating, so the total KE = the linear KE + the rotational KE

4. Find the total kinetic energy of a rolling bowling ball that has a mass of 8 kg and a radius of 0.19 m moving at 16 m/s.

v = rω

ISphere = 2/5 MR2

ICylinder = 1/2 MR2

IRing = MR2

IStick thru center = 1/12 ML2

IStick thru end = 1/3 ML2


Recall: E1 = E2

5. Find the height a rolling bowling ball that has a mass of 4 kg and a radius of 0.15 m moving at 7 m/s can roll up a hill.

v = rω

ISphere = 2/5 MR2

ICylinder = 1/2 MR2

IRing = MR2

IStick thru center = 1/12 ML2

IStick thru end = 1/3 ML^2


Hint: force at a distance is torque

6. A coke can is suspended by a string from the tab so that it spins with a vertical axis. A 17 N perpendicular force at the edge causes rotation. Find the angular acceleration if the can has a radius of 5 cm and a mass of 929 grams.

Hint: force at a distance is torque

ISphere = 2/5 MR2

ICylinder = 1/2 MR2

IRing = MR2

IStick thru center = 1/12 ML2

IStick thru end = 1/3 ML2

Solutions

Expert Solution

All the problems are standard rotarional dynamics problems and can be solved by using standard formulas in terms of moment of inertia and angular velocity. All the 6 parts are solved step by step. please find the attached solution and provide your valuable feedback.

genius_generous answered 2 years ago
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