An ultracentrifuge accelerates from rest to 100,000 rpm in 2.00 min. What is the tangential acceleration of a point 9.50 cm from the axis of rotation? Your answer should be given in m/sec squared.
Tangential acceleration = angular acceleration * radius
How would I find this?
angular acceleration = (1E5 * 2 * π) / (2 * 60)
... rad/s^2
the radius is ... .095 m
That gives me 497.42...it's wrong
change in angular velocity
= 10^5 * 2 pi radians/60 seconds
change in time = 2 * 60 seconds
so I get
10^5 * 2 *pi /(120*60)
multiply that by .095
or just divide previous answer by 60
is it a significant figure issue?
you've got 5 in your answer
but there is only one in the rpm data
To find the tangential acceleration of a point, you need to calculate the angular acceleration and multiply it by the radius. Here's how you can do it step by step:
1. Convert the given rotational speed from revolutions per minute (rpm) to radians per second (rad/s). Since 1 revolution is equal to 2π radians, you can use this conversion factor:
100,000 rpm * (2π rad/1 revolution) = 100,000 * 2π rad/min
2. Convert the minutes to seconds:
2.00 min * (60 s/1 min) = 120 s
Now you have the angular velocity in rad/s.
3. Calculate the angular acceleration (α) using the formula:
Angular acceleration (α) = change in angular velocity / time
Since the initial angular velocity is zero (since it starts from rest), you can use the final angular velocity:
Angular acceleration (α) = (final angular velocity - initial angular velocity) / time = (100,000 * 2π rad - 0 rad) / 120 s
4. Now you have the angular acceleration (α) in rad/s^2. Next, you need to multiply it by the radius.
Tangential acceleration = α * radius
In this case, the radius is given as 9.50 cm, which needs to be converted to meters:
9.50 cm * (1 m/100 cm) = 0.095 m
Tangential acceleration = α * 0.095 m
Now you can insert the value of α to find the tangential acceleration in m/s^2.