Circular Motion of a 8.0cm CD: Finding Speed and Revolution Using Kinematics

[reverse]

A magnetic computer disk 8.0 cm in diameter is initially at rest. A small dot is painted on the edge of the disk. The disk accelerates at 600 rad/ s^2 for 1/2 s, then coasts at a steady angular velocity for another 1/2 s . a) What is the speed of the dot at t = 1.0 s?
b)Through how many revolutions has it turned?


for a) i kept getting the answer wrong:
i did :
d=8.0cm
so r=4.0 cm
ti=0s
tf=0.5s
a=600 rad/s^2

vi=(2)(pi)(4.0cm) / 1.0s

so; vi=25m/s


and for part b)
i think you have to use the kinematic equation after you get vi.. I'm not sure tho.. am i right?? please help. thanks in advance!

 

[Philosophaie]

For part a) What is the velocity after .5s - v=a*t
then coasts at a steady angular velocity for another .5 s - same Angular velocity as accelerated to

 

[baba89]

As a scientist, it is important to be precise and accurate in our calculations. Let's break down the problem step by step to find the correct answers.

a) To find the speed of the dot at t = 1.0 s, we can use the formula v = u + at, where v is the final velocity, u is the initial velocity, a is the acceleration, and t is the time. In this case, the initial velocity is 0 m/s since the disk was initially at rest. The acceleration is given as 600 rad/s^2 and the time is 1.0 s. So, we can plug in these values to get:

v = 0 + (600 rad/s^2)(1.0 s)
v = 600 rad/s

However, this is the angular velocity, not the linear speed. To convert from angular velocity to linear speed, we use the formula v = ωr, where ω is the angular velocity and r is the radius. So, we can plug in the values we have to get:

v = (600 rad/s)(4.0 cm)
v = 2400 cm/s

Remember to convert the radius from cm to m to get the final answer in m/s. So, the speed of the dot at t = 1.0 s is 24 m/s.

b) To find the number of revolutions, we can use the formula θ = ωt + 1/2at^2, where θ is the angle turned, ω is the angular velocity, a is the angular acceleration, and t is the time. In this case, the angular velocity is constant at 600 rad/s, so we do not need to use the second term in the equation. The time is 1.0 s. So, we can plug in the values to get:

θ = (600 rad/s)(1.0 s)
θ = 600 rad

To convert from radians to revolutions, we use the conversion factor 2π rad = 1 revolution. So, we can divide the angle by 2π to get the number of revolutions:

θ = (600 rad) / (2π rad)
θ = 95.5 revolutions

Therefore, the dot has turned approximately 95.5 revolutions in 1.0 s.

In conclusion, the speed of the dot at t = 1.0 s is 24 m/s