Question #108631

On an interstate highway, you are traveling at 30 m/sec. The diameter of the wheels is 50 cm. How fast are the wheels rotating in revolutions/sec?

c. On your vacation, you visited several casinos in Las Vegas, and in one of them, you stopped by a roulette table. You observed that roulette wheel takes about 25 seconds to come to a stop, and it completed 40 revolutions in this time. How fast was it rotating at the very beginning before starting to slow down?

2.

a. Provide a mathematical definition of momentum, and provide its unit in the

MKS system of units.

b. In a game of billiards, there are usually 11 identical balls. In this problem,

we concentrate on two of them. The first one is hit by the player and moves at a speed of 14 m/sec, and it collides with a second stationary ball. The two balls stick together. What is the speed of the balls after the collision?

c. On your vacation, you visited several casinos in Las Vegas, and in one of them, you stopped by a roulette table. You observed that roulette wheel takes about 25 seconds to come to a stop, and it completed 40 revolutions in this time. How fast was it rotating at the very beginning before starting to slow down?

2.

a. Provide a mathematical definition of momentum, and provide its unit in the

MKS system of units.

b. In a game of billiards, there are usually 11 identical balls. In this problem,

we concentrate on two of them. The first one is hit by the player and moves at a speed of 14 m/sec, and it collides with a second stationary ball. The two balls stick together. What is the speed of the balls after the collision?

Expert's answer

*On an interstate highway, you are traveling at 30 m/sec. The diameter of the wheels is 50 cm. How fast are the wheels rotating in revolutions/sec?*

*From,*

"\\omega=\\frac{v}{r}"

where v is the velocity r is the radius and "\\omega" is the angular velocity

"\\omega=\\frac{v}{r}=\\frac{30}{0.25}=120rads^{-1}=>\\frac{120}{2\\pi}=19.09rev\/sec"

*c. On your vacation, you visited several casinos in Las Vegas, and in one of them, you stopped by a roulette table. You observed that roulette wheel takes about 25 seconds to come to a stop, and it completed 40 revolutions in this time. How fast was it rotating at the very beginning before starting to slow down?*

"\\theta=\\omega_0\\times t+\\frac{1}{2}\\alpha t^2 \\to(1)"

"\\omega=\\omega_0+{}\\alpha t\\to(2)"

where ,"\\theta" is the angle it rotated ,"\\omega_0" is the intial angular velocity and "\\alpha" is the angular *acceleration*

From 2,

"0=\\omega_0+\\alpha (25) => \\alpha=-\\frac{\\omega_0}{25}"

substituting to (1)

"40\\times2\\pi=\\omega_0\\times25+0.5\\times (-\\frac{\\omega_0}{25})\\times25^2"

solving this gives,

"\\omega_0=20.10rad\/s"

*a. Provide a mathematical definition of momentum, and provide its unit in the*

*MKS system of units.*

**Momentum** is a vector quantity that is the product of the mass and the velocity of an object or particle.

"Momentum (P) = Mass(m) \\times Velocity (V)"

units in MKS = "kg\\ ms^{-1}"

*b. In a game of billiards, there are usually 11 identical balls. In this problem,*

*we concentrate on two of them. The first one is hit by the player and moves at a speed of 14 m/sec, and it collides with a second stationary ball. The two balls stick together. What is the speed of the balls after the collision?*

since balls are identical the mass of the balls are equal,

"m_1=m_2=m"

From the momentum conservation principle, let "V_1" be the first ball speed and "V_2" be the speed of the two balls after collision.

"m_1 V_1=(m_1+m_2) V_2 \\\\\nmV_1=(2m)V_2\\\\\nV_2=\\frac{V_1}{2}=\\frac{14}{2}=7\\ m\/sec"

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