Final answer:
To calculate the angular velocity given the linear velocity and radius, use the formula ω = v/r. The wheel's angular velocity is 40.0 rad/s. After 25.0 seconds, the wheel has made approximately 159.155 revolutions.
Step-by-step explanation:
The question relates to the topic of rotational motion in physics, specifically involving angular velocity and converting between linear velocity and revolutions. Given a point on the rim of a spinning wheel with a radius of 45.0 cm and a linear velocity of 18.0 m/s, we can find the angular velocity using the formula ω (angular velocity) = v/r, where v is the linear velocity and r is the radius of the wheel.
First convert the radius to meters: 45.0 cm = 0.450 m. Then, calculate the angular velocity: ω = 18.0 m/s / 0.450 m = 40.0 rad/s.
To find the number of revolutions the wheel has made after 25.0 s, we first find the total angular displacement by multiplying the angular velocity by the time: 40.0 rad/s * 25.0 s = 1000 rad. Since there are 2π radians in a revolution, the total number of revolutions is 1000 rad / (2π) ≈ 159.155 revs.
Calculation Summary
- Convert radius from cm to m: 45.0 cm = 0.450 m
- Calculate angular velocity: ω = v/r = 18.0 m/s / 0.450 m = 40.0 rad/s
- Calculate total angular displacement after 25.0 s: 40.0 rad/s * 25.0 s = 1000 rad
- Convert radians to revolutions: 1000 rad / (2π) ≈ 159.155 revs