machine part

👨🏻‍🏫 學術台其他 - 科學

Anonymous

2012-11-02 12:48 am

A machine part has the shape of a solid uniform sphere of mass 230g and
diameter 2.70cm . It is spinning about a frictionless axle through its center,
but at
one point on its equator it is scraping against metal, resulting in a friction
force
of 0.0200N at that point.

1. Find its angular acceleration. Let the direction the sphere is spinning be the
positive sense of rotation.

2. How long will it take to decrease its rotational speed by 23.0 rad/s?

更新1:

Q1's unit should be in rad/s^2 Q2 is wrong.

更新2:

The system told me the answer is wrong.

更新3:

Q1 is -16.1m/s

更新4:

Q1 is -16.1 rad/s^2

更新5:

Q2: 1.43s

回答 (2)

用戶25975

2012-11-05 7:59 pm

✔ 最佳答案

1) The moment of inertia of the sphere is (2/5) x 0.23 x (0.027/2)2 = 1.6767 x 10-5 kg m2

Torque resulting from the friction = 0.027/2 x 0.02 = 2.7 x 10-4 N m

Hence angular acceleration = -(2.7 x 10-4)/(1.6767 x 10-5) = -16.1 rad/s2

2) 23/16.1 = 1.43 s

參考: 原創答案

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天同

2012-11-02 1:08 am

Moment of inertia of sphere = (2/5).(230/1000).(0.027/2)^2 Kg.m^2
= 1.677 x 10^-5 kg.m^2
Torque acted on the sphere = -0.02 x (0.027/2) N.m = -2.7 N.m
Hence, angular acceleration = -2.7/1.677x10^-5 s^-2 = -1.61 x 10^5 s^-2

Time taken = 23/1.61x10^5 s = 1.43 x 10^-4 s

2012-11-02 00:29:52 補充：
"radian" is a dimensionless quantity.
How do you convince yourself that the answer is wrong?

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