Examples A wheel is initially turning with an angular velocity of 25 rad/s t. It

Question

Examples A wheel is initially turning with an angular velocity of 25 rad/s t. It is slowed to a stop with constant angular acceleration. It takes 15 seconds to come to a full stop. What is the value of the acceleration? 1. A car is traveling down the highway at about100 kph without slipping. One of the wheels has a radius of about30 cm. What is the angular speed of the wheel? 2. The same car as in question 2 travels for 100 km without slipping. How many revolutions has the wheel made during this trip? 3. 4. The wheel of the car in question 2 has a moment of inertia of 0.35 kg m2. What is the magnitude of the angular momentum of the wheel?

Explanation / Answer

1.

Using equation

wf = wi + alpha*t

wi = initial angular velocity = 25 rad/sec

wf = 0 rad/sec

t = 15 sec

So

alpha = angular accelration = ?

alpha = (wf - wi)/t

alpha = (0 - 25)/15

alpha = -1.67 rad/sec^2 i

2.

V = w*r

w = V/r

V = 100 kph = 27.78 m/sec

r = 30 cm = 0.3 m

So,

w = 27.78/0.3 = 92.6 rad/sec

3.

s = r*theta

theta = s/r

theta = 100 km/0.3 = 333333.33 rad

1 rad = 1/(2*pi) rev

theta = 333333.33/(2*pi) = 53051.65 rev

4.

Angular momentum is given by;

L = I*w

L = 0.35*92.6 = 32.41 kg-m/sec

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