a disc of radius 5.70 cm rotates about its axis and a point 1.90 cm from the center of the disc moves 34.5 cm in 12.2 s .calculate the angular velocity of the disc.
1.49 rad/s
To calculate the angular velocity of the disc, we can use the formula:
Angular velocity (ω) = Linear velocity (v) / Radius (r)
Given that the point on the disc moves a linear distance of 34.5 cm in 12.2 s and is located 1.90 cm from the center of the disc, we can calculate the linear velocity as follows:
Linear velocity (v) = Linear distance (d) / Time (t)
v = 34.5 cm / 12.2 s
v ≈ 2.83 cm/s
Now, we need to calculate the angular velocity. Remember that the linear velocity is the tangential velocity at a given point on a rotating object.
Angular velocity (ω) = v / r
ω = 2.83 cm/s / 1.90 cm
ω ≈ 1.49 rad/s
Therefore, the angular velocity of the disc is approximately 1.49 rad/s.