Answered step by step
Verified Expert Solution
Link Copied!

Question

1 Approved Answer

5. *Half-sphere tippy top. Set up the integrals and calculate the moment of inertia of a half-sphere tippy top about its symmetry axis. [Answer:

imageimage

5. *Half-sphere tippy top. Set up the integrals and calculate the moment of inertia of a half-sphere tippy top about its symmetry axis. [Answer: Ma] 6. **Tippy top. A tippy top is a nearly spherical top that turns itself upside-down when spun on a smooth table. The torque that causes the top to flip is due to a small frictional force at the point of contact with the table. This frictional force is parallel to the table, opposing the velocity of slipping, as illustrated in the figure. The top itself consists of a sphere with a portion removed to expose the stem." The stem is used to spin the top. Initially the stem points up. When the top is released, the angle between the stem and the vertical steadily increases until the top flips over. View the video that comes up first in a google search for "tippe top SMU." (a) Order the moments of inertia along your three principal axes. (Which is larger, which is smaller, which is equal?) Select 3 as your symmetry axis. Select the other axes so initially w = wo (sin 0, 0, cos 0). Sketch these principal axes on top of the figure. (b) Use Euler's equation for one of your axes to show that ~ F/(Iwo). [Hint: differentiate w to get something that depends upon 0.] (c) Show that the top takes approximately t~ :2 Rwo/(5g) to flip over. (d) Based on the video, write down reasonable estimates for R, wo and and use these to estimate the predicted flipping time. How long does it take to flip in the video? Is your estimate the correct order of magnitudee? (e) As the video states, the top slows down when it flips over. Neglecting dissi- pation, use energy conservation to estimate the ratio of the angular velocity Wup to the initial angular velocity wo immediately after tipping in terms of the change in height of the top's center of mass h and other parameters. X Low Pressure Area Lift Positive Pressure Area WO = wp w * CM Center of curvature R friction Figure 1: Tippy top.

Step by Step Solution

There are 3 Steps involved in it

Step: 1

blur-text-image

Get Instant Access to Expert-Tailored Solutions

See step-by-step solutions with expert insights and AI powered tools for academic success

Step: 2

blur-text-image

Step: 3

blur-text-image

Ace Your Homework with AI

Get the answers you need in no time with our AI-driven, step-by-step assistance

Get Started

Recommended Textbook for

Physics for Scientists and Engineers A Strategic Approach with Modern Physics

Authors: Randall D. Knight

4th edition

978-0134092508, 134092503, 133942651, 978-0133942651

More Books

Students also viewed these Physics questions

Question

Why is there hardly any space in space for GEOs?

Answered: 1 week ago

Question

Establish identity. cos( + k) = (-1)k cos , k any integer

Answered: 1 week ago