Question

A wheel is rotating about an axis that is in the z-direction. The angular velocity ?z is ?6.00rad/sat t=0, increases linearly with time and is +8.00rad/s at t=7.00s. We have taken counterclockwise rotation to be positive

Q1: Is the angular acceleration during this time interval positive or negative?

Q2: Find the duration of the time interval when the speed of the wheel is increasing.

Q3: Find the duration of the time interval when the speed of the wheel is decreasing.

Q4: What is the angular displacement of the wheel at t=7.00s?

Answer 1

here,

initial angular velocity , w0 = - 6 rad/s

final angular velocity , w = 8 rad/s

time taken , t1 = 7 s

a)

let the angular accelration be alpha

w = w0 + alpha * t1

8 = - 6 + alpha * 7

alpha = 2 rad/s^2

b)

let the time taken to attain angular velocity zero be w2

0 = - 6 + alpha * t2

t2 = 3 s

so, the duration of the time interval when the speed of the wheel is increasing is from 3s to t = 7 s

c)

the duration of the time interval when the speed of the wheel is decreasing is from t =0 s to t = 3 s

d)

the angular displacement of the wheel , theta = w0 * t1 + 0.5 * alpha * t1^2

theta = - 6 * 7 + 0.5 * 2 * 7^2 rad

theta = 7 rad