Abicycle wheel is rotating at 49 rpm when the cyclist begins to pedal harder, giving the wheel a constant angular acceleration of 0.45 rad/s2 . what is the wheel's angular velocity, in rpm, 9.0 s later?

The bicycle wheel's angular velocity, in rpm is 87.68 rpm.

Given the following data:

Conversion:

1 rpm = 0.1047 rad/s

49 rpm = X rad/s

Cross-multiplying, we have:

×

X = 5.1303 rad/s

To find the bicycle wheel's angular velocity, in rpm, we would use the first equation of kinematics:

Where:

Substituting the given parameters into the formula, we have;

Final angular velocity = 9.1803 rad/s

Next, we would convert the value in rad/s to rpm:

Conversion:

1 rpm = 0.1047 rad/s

X rpm = 9.1803 rad/s

Cross-multiplying, we have:

X = 87.68 rpm.

Final angular velocity = 87.68 rpm.

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Angular velocity,

Explanation:

It is given that

Initial angular velocity of the wheel,

Since, 1 revolutions per minute =  0.10471 radians per second

Angular acceleration of the wheel,

Time taken, t = 9 s

Let is the final velocity of the wheel 9 seconds later. Using the equation of kinematics to find it :

So, the final angular velocity of the wheel is 9.180 rad/s. Hence, this is the required solution.

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