Question

A bicycle tire is spinning counterclockwise at 3.00 rad/s. During a time period Δt = 2.30 s, the tire is stopped and spun in theopposite (clockwise) direction, also at 3.00 rad/s. Calculate the change in the tire's angular velocity Δω and the tire's averageangular acceleration α. (Indicate the direction with the signs of your answers.)

Answer 1

Δω = -6.00 rad/s

α = -2.61 m/s²

Step-by-step explanation:

Step 1: Data given

A bicycle tire is spinning counterclockwise at 3.00 rad/s

Δt = 2.30 s

In theopposite (clockwise) direction, also at 3.00 rad/s

Step 2: Calculate the change in the tire's angular velocity Δω

Δω = ωf - ωi

ωf = - 3.00 rad/s

ωi = 3.00 rad/s

Δω = ωf - ωi = -3.00 - 3.00 = -6.00 rad/s

Step 3: Calculate the tire's average angular acceleration α

α = Δω / ΔT

α = -6.00 rad/s /2.30s

α = -2.61 m/s²

A negative angular acceleration means a decreasing angular velocity