Circular & Rotational Motion Mini-(Pseudo) Activities These short activities are

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Circular & Rotational Motion Mini-(Pseudo) Activities These short activities are designed to allow you to apply your knowledge about the kinematics of circular and rotational motion of objects in order to anlayze data for the scenarios described in each of the mini-(pseudo) activities below. Shaft Encoder Suppose that youve been assigned the task of using a shaft encoder - a device that measures the angle of a shaft or axle and provides a signal to a computer -to analyze the rotation of an engine crankshaft under certain conditions. The table below lists the crankshaft's angles over a 0.6s interval. Determine whether or not the crankshaft is rotating with uniform circular motion. If so, determine what its angular velocity is in rpm. If not, determine whether the angular acceleration is positive or negative, as well as the approximate magnitude of the angular acceleration. Time (seconds) Angle (radians) 0.0 2.0 3.2 4.3 5.3 6.1 7.0 0.1 0.2 0.3 0.5 0.6 Automobile Engine Crankshaft with no other cars in sight, you decide to measure the angular acceleration of t memory, you are able to read the your engine's crankshaft while braking gently. Having excellen tachometer every 1 s and remember seven values long enough to later write them down. The table below shows your data. Determine the magnitude of the crankshaft's angular acceleration (in units of ). Time (seconds) Angular Velocity (pm 3010 2810 8450 2250 1940 1510

Explanation / Answer

Here, in shaft encoder, after each 0.1 seconds from t=0, the angular displacement / time taken is calculated to find angular speed(w) at all times from t=0 to t=0.6 (i.e. w0 to w6)

So, w0= angle /time= 0/0= 0

similarly, w1= 2/0.1= 20,

w2= 3.2/0.2= 16

w3= 4.3/0.3= 14.33

w4= 5.3/0.4= 13.25

w5= 6.1/0.5= 12.2

w6= 7/0.6= 11.67

Since w0= 0, it is at reat initially. Also, w1 is highest and then onwards w is decreasing. Now, approximate value of angular acceleration is net change in angular speed / time interval. For finding change in angular speed, final speed is w6 but initial speed is w1 because w0 is when it is stopped, after which it rotates and keep slowing down with the acceleration to be found.

So, approximate value of angular accelaration= angular speed w6- angular speed w1/ time taken= 11.67-20/ 0.6-0.1= -16.66 rad/s^2

So , angular accelaration is negative.

Here, in engine crankshaft, speed is converted from rpm to rad/s^2 by using w= 2*pi*rpm/ 60= 0.1047*rpm

its angular acceleration is given by a= final speed- initial speed/ time taken= 1510*0.1047- 3010*0.1047/ 6-0 = -2.6175 rad/s^2

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