A) Initially (t=0) a 5kg wheel was spinning at 4.3 rad/sec. After it has complet

Question

A) Initially (t=0) a 5kg wheel was spinning at 4.3 rad/sec. After it has completed six turns, it is spinning at 2.70 rad/sec. Assuming the angular speed decreased at a constant rate, find the angular acceleration a of the wheel.

*I had thought the answer was (4.3-2.7)/(6-0)=0.2667 but that is not correct.

B) A spinning wheel has an initial angular speed of 3.4 rad/s (at t=0) and a later angular speed of 1.3 rad/s, such that the angular speed is decreasing at a constant rate of 0.11 rad/s^2. How much time (meansured from t=0) will this wheel take to stop?

Any help would be greatly appreciated!

Explanation / Answer

here,

A)

mass of the wheel , m = 5 kg

initial angular speed , w0 = 4.3 rad/s

final angular speed , w = 2.7 rad/s

number of rotation ,n =6

theta = 6 * 2*pi = 37.68 rad

let the angular accelration be a

using third equation of motion

w^2 - w0^2 = 2*theta*a

2.7^2 - 4.3^2 = 2*37.68*a

a = - 0.15 rad/s^2

the angular accelration off the wheel is - 0.15 rad/s^2

B)

initial angular speed , w0 = 3.4 rad/s

final angular speed , w = 0 rad/s

deaccelration , a = 0.11 rad/s^2

let the time be t

using first equation of motion

w = w0 + a*t

0 = 3.4 - 0.11*t

t = 30.91 s

the time taken to stop the wheel is 30.91 s

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