The wagon is moving in the +x direction. Which way will the wheels rotate? What is the usual convention for the sign of a rotation in planar co-ordinates?goonking said:
wheels will rotate clockwise.haruspex said:
Yes, and what is usually taken as the positive direction for a rotation in the plane?goonking said:
I thought it didn't matter which direction you set to be positive or negative.haruspex said:
The standard convention, e.g. in polar co-ordinates, is anticlockwise positive.goonking said:
A radian is a unit of measurement for angles, representing the amount of rotation an object undergoes around a fixed point. It is defined as the angle created by two radii of a circle that intercept an arc equal in length to the radius.
A negative 126 radian measures an angle that is equivalent to rotating counterclockwise by 126 radians, or about 7255 degrees. It is important to note that angles measured in radians can be either positive or negative, depending on the direction of rotation.
To calculate a negative 126 radian, you can use the formula:
angle in radians = (angle in degrees * pi) / 180
In this case, it would be:
(-126 * 3.14159) / 180 = -2.19911 radians
Yes, an angle can be both positive and negative in radians. This is because radians measure the direction of rotation, and an angle can rotate in either a clockwise (positive) or counterclockwise (negative) direction.
To convert radians to degrees, you can use the formula:
angle in degrees = (angle in radians * 180) / pi
In this case, it would be:
(-2.19911 * 180) / 3.14159 = -126 degrees