The blades in a blender rotate at a rate of 6500 rpm. When the motor is turned off during operation, the blades slow to rest in 2.6 s.
1. What is the angular acceleration as the blades slow down?
Answer should be negative
The rpm first needs to be converted to rad/s, by multiplying by 2 pi/60
The angular deceleration rate is
[6500*(2 pi)/60]/2.6 rad/s^2
223.884
To find the angular acceleration, we need to use the formula:
Angular acceleration (α) = (Final angular velocity - Initial angular velocity) / Time
Here, the initial angular velocity is given as 6500 rpm, which we need to convert to rad/s. And the final angular velocity is 0 rad/s, as the blades come to rest. The time taken for the blades to stop spinning is given as 2.6 seconds.
Step 1: Convert the initial angular velocity from rpm to rad/s
Since 1 revolution equals 2π radians, we can convert rpm to rad/s by multiplying by 2π/60.
Initial angular velocity = 6500 rpm * (2π rad/1 revolution) * (1 revolution/60 s)
Initial angular velocity = 6500 rpm * (2π/60) rad/s
Step 2: Calculate the angular acceleration
Angular acceleration = (Final angular velocity - Initial angular velocity) / Time
Angular acceleration = (0 rad/s - Initial angular velocity) / 2.6 s
Angular acceleration = (0 rad/s - 6500 rpm * (2π/60) rad/s) / 2.6 s
Now, let's calculate the angular acceleration:
Angular acceleration = (0 - 6500 * (2π/60)) / 2.6
Angular acceleration = (-6500 * (2π/60)) / 2.6
Angular acceleration = -404.142 rad/s² (rounded to three decimal places)
Therefore, the angular acceleration as the blades slow down is approximately -404.142 rad/s². The negative sign indicates that the blades are decelerating or slowing down.