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Classical Mechanics Level 2

A bicycle is moving at 10 m/s. What is the angular speed to its nearest integer value in radians per seconds of its tires if their radius is 30 cm?

Image credit: Wikipedia Agnieszka Kwiecien


The answer is 33.

Omar Nader by Omar Nader , 23, Egypt

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5 solutions

Omar Nader
Sep 14, 2014

the linear speed is related angular speed of its tires if their radius is 30 cm v = w r where v =10m/s r=30=0.3m then w =v/r=10/0.3=33

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oh, engaging

Thớt Tuấn - 6 years, 8 months ago

As we know, rw=v ,where r is radius and w and v are angular speed and linear speed respectively.hence w=v/r=10/.3=33.that is how we get the answer.

PIU DAS - 6 years, 8 months ago
Preetam Kandula
Jul 24, 2016

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In the last figure the angle is wrong I mean the angle angle that u calculated not the angle of incline.

Preetam Kandula - 4 years, 10 months ago

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thank you for checking my solution.

A Former Brilliant Member - 4 years, 10 months ago

Well anyways there is another mistake in you solution and now I'm uploading it in these solutions as I can't find a way to post a pic as a comment

Preetam Kandula - 4 years, 10 months ago

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thank you very much brother, now i understood that i have taken the y-displacement wrong, thank you again.

A Former Brilliant Member - 4 years, 10 months ago

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Anytime bro.. :p

Preetam Kandula - 4 years, 10 months ago

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@Preetam Kandula – hey brother can you check out this : https://brilliant.org/discussions/thread/little-problem/ . need help . plz tell my mistake.

A Former Brilliant Member - 4 years, 10 months ago

Convert 10 m/s into 1000 cm/s. Then determine the circumference of the tire using the formula c=2pi(r) to obtain 60(pi) cm. Then divide the speed of the tire in cm/s by the circumference of the tire in cm/rotation to obtain the number of rotations/s. Given that each rotation is 2pi radians/rotation, we can then multiply by that. This brings us to 33.3 radians/s.

This particular solution can be done with limited prior knowledge. It requires knowing the formula for circumference, knowing that there are 2pi radians in a circle, and knowledge of unit conversions.

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Jaswanth Varma
Sep 21, 2014

as we know the relation between the velocity "v" and the angular velocity "w" is given by the realtion 'v=rw' , substitute the given values to get the result which is equla to (10*100)/30=33.33. here we multiplied with 100 so as to convert the units into cm.

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