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# Answer to Question #108631 in Mechanics | Relativity for Shavonne Fraley

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?
1
2020-04-09T09:29:20-0400

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

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,

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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