Plane Curvilinear Motion: n-t Coordinates - Example Problem 3.3-9
The angular speed of a 15 in diameter circular saw blade is 1500 rpm when the power to the saw is turned off. The speed decreases at a constant rate until the blade comes to rest 15 seconds later. Determine the acceleration of a saw tooth, on the circumference of the saw blade, 5 seconds after the power is turned off.
Given:
- D = 15 in = 0.625 ft
- (dθ/dt)o = 1500 rpm
- (dθ/dt)f = 0
- Δt = 15 s
- (d 2θ/dt 2) = constant
Find:
- a @ t = 5 s
Solution:
Video solution:
The following video walks you through the solution to this problem. It is suggested that you try solving the problem first and then, if you have difficulties with the solution, watch the video for help.
Interactive solution:
Since the distance of the tooth from the center of rotation does not change, we are dealing with circular motion. This means that the radius of curvature is constant and the velocity and acceleration may be expressed in terms of the angular velocity and angular acceleration.
Convert the radius into units of feet.