Answered

A bicycle wheel is rotating at 50 rpm when the cyclist begins to pedal harder, giving the wheel a constant angular acceleration of 0.46 rad/s2. How many revolutions does the wheel make during this time?

Answer :

Answer:

A. 9.84 rad/sec or

= 93.93 rev/min

B. 12 turns.

Explanation:

ωf = ω° + αt

Where,

t = 10s

ω° = initial speed in rad /s

= 50 rev/min(rpm)

Converting rpm to rad/sec,

50 * 2π/60

= 5.236 rad/s

α = angular acceleration = 0.46 rad/s^2

ωf = final angular velocity

ωf = 5.236 + 0.46*10sec

ωf = 9.84 rad/sec or

= 93.93 rev/min

B.

θ = ω°*t + 1/2*(α*t^2)

Where,

θ = angular displacement in rad.

θ = 5.236 * 10 + 0.5 * 0.46 * (10)^2

= 52.36 + 23

= 75.36 rad n turns

= 75.36/2π

= 12 turns

The number of revolutions of the bicycle wheel is 50 revolutions.

What is angular speed?

The angular speed of an object is the angular displacement of the object per a given time.

The given parameters;

  • Angular speed = 50 rev/min
  • Angular acceleration = 0.46 rad/s²

The angular speed of the bicycle wheel is 50 revolutions per min

Thus, we can conclude that the number of revolutions of the bicycle wheel is 50 revolutions.

Learn more about angular speed here: https://brainly.com/question/6860269

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