A person is riding a bicycle, and its wheels have an angular velocity of 22.0 rad/s....

A person is riding a bicycle, and its wheels have an angular velocity of 22.0 rad/s. Then, the brakes are applied and the bike is brought to a uniform stop. During braking, the angular displacement of each wheel is 12.9 revolutions. (a) How much time does it take for the bike to come to rest? (b) What is the anguar acceleration (in rad/s2) of each wheel?

Solutions

Expert Solution

Initial angular velocity of the wheel = ₁ = 22 rad/s

Final angular velocity of the wheel = ₂ = 0 rad/s

Number of revolutions made by the wheel before coming to a stop = n = 12.9 rev

Angular displacement of the wheel =

= 2n

= 2(12.9)

= 81.053 rad

Angular acceleration of the wheel =

₂² = ₁² + 2

(0)² = (22)² + 2(81.053)

= -2.99 rad/s²

Negative as it is deceleration.

Time taken by the wheel to come to rest = T

₂ = ₁ + T

0 = 22 + (-2.99)T

T = 7.36 sec

a) Time taken by the bike to come to rest = 7.36 sec

b) Angular acceleration of each wheel = -2.99 rad/s²

genius_generous answered 1 month ago

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