A point (labelled P in the figure) is attached to the rim of a disk of radius 0.2 m, which can turn around an axis through its center. It is rotating counterclockwise with a speed of 2.5 m/s.
Can someone please help me solve this equation step by step?
Certainly! To solve this problem, we can use the concept of rotational motion. The main equation we will use is the angular velocity equation, which relates the linear speed of a point on a rotating object to its radial distance from the axis of rotation.
The angular velocity equation is given as:
ω = v / r,
where ω is the angular velocity (in radians per second), v is the linear speed (in meters per second), and r is the radial distance from the axis of rotation (in meters).
In this case, we are given that the linear speed v is 2.5 m/s and the radius r is 0.2 m. We need to find the angular velocity ω.
Step 1: Identify the given values:
v = 2.5 m/s
r = 0.2 m
Step 2: Plug the values into the equation:
ω = v / r
ω = 2.5 m/s / 0.2 m.
Step 3: Solve the equation:
ω = 12.5 rad/s.
So, the angular velocity of the disk is 12.5 rad/s.
Note: The radian (rad) is the standard unit for measuring angles in rotational motion. It is defined as the ratio of the arc length to the radius of curvature. In this case, the angular velocity is measured in radians per second.