A wheel spins on a horizontal axis, with an angular spped of 140rad/s and with its angular velocity pointing east. Determine the magnitude of the angular velocity after an angular acceleration of 35 rad/s^2, pointing 68 degress west of north, with a time of 4.6 seconds. I found that the magnitude of the angular velocity is 61 rad/s, but how do i determine the direction of its angular velocity west of north in degrees.
Follow the instructiuons given in my previous answer
To determine the direction of the angular velocity west of north in degrees, you can use basic trigonometry.
1. Start by drawing a coordinate system with north as the positive y-axis and west as the negative x-axis.
2. The given direction of 68 degrees west of north can be represented as an angle θ measured from the positive y-axis in a clockwise direction.
3. Convert the angle θ from degrees to radians by multiplying it by π/180.
θ_radians = (68 * π) / 180 = 1.19 radians (rounded to two decimal places).
4. Since west of north is in the third quadrant of the coordinate system, the direction can be represented as -1.19 radians.
5. Add the angular acceleration (35 rad/s^2) with the initial angular velocity (140 rad/s) multiplied by the time (4.6 seconds) to get the final angular velocity.
Final angular velocity = Initial angular velocity + (Angular acceleration * Time)
= 140 rad/s + (35 rad/s^2 * 4.6 s)
= 140 rad/s + 161 rad/s
= 301 rad/s.
6. Finally, combine the magnitude of the angular velocity (61 rad/s) and the direction (-1.19 radians) to fully describe the angular velocity.
Angular velocity = 61 rad/s at an angle of -1.19 radians (or equivalently, -68 degrees) west of north.