A wheel initially (at t = 0) has an angular velocity of 18 rad/s.It has a constant angular acceleration with a magnitude of 2.0 rad/s2 and at t = 0 the angular velocity is decreasing.At what time t is the angular velocity equal to 18 rad/s in the direction opposite to the initial angular velocity?Express your answer in seconds.
Question
A wheel initially (at t = 0) has an angular velocity of 18 rad/s.It has a constant angular acceleration with a magnitude of 2.0 rad/s2 and at t = 0 the angular velocity is decreasing.At what time t is the angular velocity equal to 18 rad/s in the direction opposite to the initial angular velocity?Express your answer in seconds.
Solution
To solve this problem, we need to find the time at which the angular velocity of the wheel is equal to 18 rad/s in the opposite direction of the initial angular velocity.
Given: Initial angular velocity, ω₀ = 18 rad/s Angular acceleration, α = -2.0 rad/s² (negative sign indicates decreasing angular velocity)
We can use the following kinematic equation to find the time, t:
ω = ω₀ + αt
Substituting the given values, we have:
18 rad/s = 18 rad/s + (-2.0 rad/s²) * t
Simplifying the equation, we get:
0 = -2.0 rad/s² * t
Since the angular velocity is decreasing, it will eventually reach 18 rad/s in the opposite direction. This means that the time, t, will be positive.
To find t, we can rearrange the equation:
t = 0 / (-2.0 rad/s²)
Since any number divided by 0 is undefined, we cannot determine the exact time at which the angular velocity becomes 18 rad/s in the opposite direction.
Similar Questions
A wheel initially has an angular velocity of 20.0 rad/s, but it is slowing down at a rate of 2.0 rad/s2. By the time it stops, how many revolutions will it have turned through?
Suppose a wheel is initially rotating at 10.0 rad/s while undergoing constant angular acceleration reaching a speed of 30.0 rad/s after 20.0 seconds have elapsed. How long after the initial time has the wheel undergone half of the angular displacement that it will have gone through during the entire 20.0 second interval?Select one:a.10.0 sb.15.0 sc.14.2 sd.12.4 s
A Ferris wheel, rotating initially at an angular speed of 0.16 rad/s, accelerates over a 8.0-s interval at a rate of 0.040 rad/s2. What is its angular speed after this 8.0-s interval?Select one:a.0.48 rad/sb.0.24 rad/sc.0.32 rad/sd.1.6 rad/se.0.05 rad/s
A wheel makes 20 revolutions per minute. Find the angular velocity.
A rotating flywheel slows down at a constant rate due to friction in its bearings. After 1.00 min, its angular velocity has diminished to 0.928 of its initial value ω𝜔. At the end of the fifth minute what is the angular velocity in terms of the initial value? Do not enter unit.
Upgrade your grade with Knowee
Get personalized homework help. Review tough concepts in more detail, or go deeper into your topic by exploring other relevant questions.