A bicycle wheel is rotating at 45 r p m when the cyclist begins to pedal harder,

Question

A bicycle wheel is rotating at 45rpm when the cyclist begins to pedal harder, giving the wheel a constant angular acceleration of 0.48rad/s2 .
1) What is the wheel's angular velocity, in rpm, 8.0s later? 2) How many revolutions does the wheel make during this time? A bicycle wheel is rotating at 45rpm when the cyclist begins to pedal harder, giving the wheel a constant angular acceleration of 0.48rad/s2 .
1) What is the wheel's angular velocity, in rpm, 8.0s later? 2) How many revolutions does the wheel make during this time? A bicycle wheel is rotating at 45rpm when the cyclist begins to pedal harder, giving the wheel a constant angular acceleration of 0.48rad/s2 .
1) What is the wheel's angular velocity, in rpm, 8.0s later? 2) How many revolutions does the wheel make during this time?

Explanation / Answer

Given:
?i (initial angular velocity)=(45 rev/min)(2?/1rev)(1min/60sec)

?i = 4.71 rad/sec

?f = final angular velocity

?f = ?i + ?t

?f = 4.71rad/sec + (0.48rad/sec^2)(8sec)

?f = 8.55 rad/sec or

(8.55 rad/sec)(1rev/2?rad)(60sec/1min)

= 81.68 rev/min ANSWER

2) ? = (?avg)(t)

? = [(?i + ?f)/2](10sec)

? = [(4.71+8.55)/2](8)

? = 53.04 rad or 53.04rad (1rev/2?rad) = 8.44 rev.

ANSWER: 8.44 rev.

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