A compact disk is 12 cm in diameter & rotates at 100 rpm when being played. The hole in the center is 1.5 cm in diameter. Find the speed in cm/min of a point on the disk & the speed of a point on the inner edge.
A revolution is 2 pi radians
So it goes w = 200 pi radians/minute
tangential speed = w r = r * 200 pi
at outside
v = 6*200 pi cm/min
at inside
v = 0.75 * 200 pi cm/min
Hi!Thanks for the answer. Might I ask what w represents?
w is Greek omega (I do not have Greek letters on my keyboard), the angular speed in radians per unit time.
If you have not studied that use:
Circumference at any radius = 2 pi r
Number of circumferences per minute = 100
so at any radius r
speed = 100 * 2 pi r = 200 pi r
Thanks again!:)
To find the speed at a point on the disk, we need to calculate the linear velocity of that point.
First, let's find the circumference of the disk by using the formula for the circumference of a circle: C = πd, where C is the circumference and d is the diameter.
C = π * 12 cm = 37.68 cm (rounded to two decimal places)
Now let's calculate the distance traveled in one minute for a point on the circumference of the disk.
Distance = Circumference * Number of revolutions per minute
Distance = 37.68 cm * 100 revolutions = 3768 cm/min
Therefore, the speed of a point on the disk is 3768 cm/min.
To find the speed of a point on the inner edge, we need to calculate the circumference of the inner edge.
Since the inner diameter is 1.5 cm, the inner radius(r) is half of that, which is 0.75 cm.
Now let's find the circumference of the inner edge using the same formula: C = πd, where C is the circumference and d is the diameter.
C_inner = π * 1.5 cm = 4.71 cm (rounded to two decimal places)
Now let's calculate the distance traveled in one minute for a point on the inner edge of the disk.
Distance_inner = Circumference_inner * Number of revolutions per minute
Distance_inner = 4.71 cm * 100 revolutions = 471 cm/min
Therefore, the speed of a point on the inner edge of the disk is 471 cm/min.