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?

3.025 revolutions

Explanation:

To solve this question firstly we need to calculate the time t

Given the angular velocity and the angular acceleration

The time t = angular velocity/angular acceleration

Converting 50rpm to rad/s

= 50 * 2π / 60

=1.67 rad/s

t = 1.67/0.46

t = 3.63s

The wheel makes 50 revolutions in one minute

Therefore in 3.63s, it will make

3.63 * 50/60

= 181.5/60

=3.025 revolutions

Approximately 3 revolutions

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