As you finish listening to your favorite compact disc (CD), the CD in the player slows down to a stop. Assume that the CD spins down with a constant angular acceleration.
a.)f the CD rotates at 500 rpm (revolutions per minute) while the last song is playing, and then spins down to zero angular speed in 2.60 s with constant angular acceleration, what is alpha, the magnitude of the angular acceleration of the CD, as it spins to a stop?
Answer= a=20.1 rad/s^2
b.)How many complete revolutions does the CD make as it spins to a stop?
Answer= 10 revolutions
I figured out a, but I had to give up and show answer on part b. The formula it told me to use was theta=theta initial + initial velocity (time) +.5(acceleration)(time^2)
I plugged in theta=0+52.36(2.6)+.5(20.1)(2.6^2) and got 204.07. However, in the hints it says that the answer is 68.1 radians which it then converted to 10 revolutions.
How did they get to 68.1 radians, and how'd they convert that to 10 revolutions?
a.)f the CD rotates at 500 rpm (revolutions per minute) while the last song is playing, and then spins down to zero angular speed in 2.60 s with constant angular acceleration, what is alpha, the magnitude of the angular acceleration of the CD, as it spins to a stop?
Answer= a=20.1 rad/s^2
b.)How many complete revolutions does the CD make as it spins to a stop?
Answer= 10 revolutions
I figured out a, but I had to give up and show answer on part b. The formula it told me to use was theta=theta initial + initial velocity (time) +.5(acceleration)(time^2)
I plugged in theta=0+52.36(2.6)+.5(20.1)(2.6^2) and got 204.07. However, in the hints it says that the answer is 68.1 radians which it then converted to 10 revolutions.
How did they get to 68.1 radians, and how'd they convert that to 10 revolutions?
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You've just fallen down the "vectors have a magnitude and direction" hole, that's all.
The acceleration is in the opposite direction to the velocity {the disc is slowing down} so the acceleration should be a = -20.1 rad/s² when you plug it in.
θ = 52.36 * 2.6 + ½ * (-20.1) * 2.6² = 68.2 rad {rounding errors}
There are 2π radians in 1 revolution, so 68.2 rad / 2π = 10.83 revolutions
That's 10 complete revolutions plus a bit!
The acceleration is in the opposite direction to the velocity {the disc is slowing down} so the acceleration should be a = -20.1 rad/s² when you plug it in.
θ = 52.36 * 2.6 + ½ * (-20.1) * 2.6² = 68.2 rad {rounding errors}
There are 2π radians in 1 revolution, so 68.2 rad / 2π = 10.83 revolutions
That's 10 complete revolutions plus a bit!