Answer :
Answer:
To find the angular velocity of the bicycle wheel, we can use the formula:
Angular velocity (ω) = Number of revolutions / Time taken = 40 rev / 60 sec = 2/3 rev/sec
Since 1 revolution (1 rev) is equal to 2π radians, we can convert the angular velocity to radians per second:
Angular velocity (ω) = (2/3) rev/sec * 2π rad/rev ≈ 4.19 rad/sec
Now to find the linear distance the wheel will travel in one revolution (circumference of the wheel):
Circumference = 2π * radius = 2π * 32 cm ≈ 201.06 cm
One revolution covers the entire circumference, so the linear distance the wheel will travel in 40 revolutions:
Linear distance = Circumference * Number of revolutions = 201.06 cm/rev * 40 rev ≈ 8042.4 cm
Therefore, the angular velocity of the bicycle wheel is approximately 4.19 rad/sec, and the linear distance the wheel will travel in 40 revolutions in 60 seconds is approximately 8042.4 cm.
