11.6: Chapter 11 Homework Problems
Exercise \(\PageIndex{1}\)
You are designing a bench grinder with an operating speed of 3600 rpm.
- If you want the grinder to reach its full operating speed in 4 seconds, what must the rate of angular acceleration be in radians per second squared?
- If the grinding wheel has a diameter of 8 inches, what will the speed of the surface of the wheel be?
- Solution
-
\(\alpha = 94.25 \ \frac{rad}{s}\)
\(v = 125.67 \ ft/s\)
Exercise \(\PageIndex{2}\)
A belt-driven system has an input at pulley A, which drives pulley B, which is attached with a solid shaft to pulley C, which drives pulley D. If the input is rotating at 60 rad/s counterclockwise, determine the angular velocity and direction of rotation for the output at D.
- Solution
-
\(\omega_D = 300 \ \frac{rad}{s}\) counterclockwise
Exercise \(\PageIndex{3}\)
The piston in a piston and crank mechanism has the velocity and acceleration shown below. Using absolute motion analysis, determine the current angular velocity and angular acceleration for the crank.
- Solution
-
\(\omega = 13.33 \ \frac{rad}{s}\) clockwise
\(\alpha = 100.16 \ \frac{rad}{s^2}\) clockwise
Exercise \(\PageIndex{4}\)
A trapdoor is being opened with a hydraulic cylinder extending at constant rate of 0.7 m/s. If the door is currently at a twenty-degree angle as shown below, what is the current angular velocity and angular acceleration for the door?
- Solution
-
\(\dot{\theta} = 0.896 \ \frac{rad}{s}, \, \ddot{\theta} = -1.246 \ \frac{rad}{s^2} \)
Exercise \(\PageIndex{5}\)
A robotic arm experiences the angular velocities and accelerations shown below. Based on this information, determine the velocity and the acceleration of the end of the arm in the \(x\) and \(y\) directions.
- Solution
-
\( v_x = 9.44 \ ft/s, \, v_y = 4.39 \ ft/s \)
\( a_x = -33.78 \ ft/s^2, \, a_y = 3.39 \ ft/s^2 \)