A limb, which is 1m long, moves through an angle of 30 degrees in 0.5 seconds.
a) What is the average angular velocity of:
i) Its end?
ii) A point 30 cm from the axis of rotation?
b) What is the linear velocity of:
i) Its end?
ii) A point 30 cm from the axis of rotation?
Already answered
To calculate the average angular velocity, we need two pieces of information: the angle through which the limb moves and the time it takes to move that angle.
a) Average angular velocity:
Step 1: Convert the given angle from degrees to radians by using the conversion factor pi/180. This is because angular velocity is typically calculated in radians per second.
Angle in radians = (30 degrees) * (pi/180) radians/degree
Step 2: Use the formula for average angular velocity:
Average angular velocity = (Change in angle) / (Time taken)
i) The angle moved by the limb is already given as 30 degrees or the equivalent in radians calculated in Step 1. The time taken is given as 0.5 seconds. Therefore, we can calculate the average angular velocity as:
Average angular velocity (end) = (30 * pi/180 radians) / (0.5 seconds)
ii) To calculate the average angular velocity at a point 30 cm from the axis of rotation, we can use similar steps. However, since the point is not at the end of the limb, we need to take into account the different distances from the axis of rotation.
The point is 30 cm from the axis of rotation, which is equivalent to 0.3 meters. Hence, we can use the same formula as above:
Average angular velocity (30 cm from axis) = (Change in angle) / (Time taken)
b) To calculate the linear velocity, we need to use the formula:
Linear velocity = Angular velocity * Radius
i) The radius in this case is 1 meter. We can use the average angular velocity (end) calculated in part (a) i) to find the linear velocity at the end of the limb:
Linear velocity (end) = Average angular velocity (end) * Radius
ii) For a point 30 cm from the axis of rotation, the radius is 0.3 meters. We can use the average angular velocity (30 cm from axis) calculated in part (a) ii) to find the linear velocity:
Linear velocity (30 cm from axis) = Average angular velocity (30 cm from axis) * Radius
By using the above formulas, you can calculate the average angular velocity and linear velocity for both cases.