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.
To calculate the angular velocity of the disc, we need to use the following formula:
Angular velocity (ω) = Linear velocity (v) / Radius (r)
First, we need to determine the linear velocity. We are given that a point 1.90 cm from the center of the disc moves 34.5 cm in 12.2 s. The linear velocity can be calculated using the formula:
Linear velocity (v) = Distance traveled (d) / Time (t)
Substituting the given values:
v = 34.5 cm / 12.2 s
Solving this equation will give us the linear velocity.
Once we have the linear velocity, we can calculate the angular velocity using the given radius of the disc:
ω = v / r
Substituting the values, we can solve for the angular velocity.
Let's calculate both the linear velocity and the angular velocity based on the given values:
Linear velocity (v) = 34.5 cm / 12.2 s = 2.836 cm/s (rounded to 3 significant figures)
Angular velocity (ω) = 2.836 cm/s / 5.70 cm = 0.498 rad/s (rounded to 3 significant figures)
Therefore, the angular velocity of the disc is approximately 0.498 rad/s.