A flywheel of 480 mm diameter is accelerated with an angular velocity of 0.4 rad/s^-2 from rest by an electric motor until it is rotating at 400 revs/minute. Calculate:
a) the time of acceleration
b) the linear speed of the rim of the flywheel
My answer for (a) is 104.7 secs, and for (b) is 10 m/s.
Appreciate if someone could check these answers if correct. If wrong, can they point me in the right direction.
TIA
Final angular speed = (angular acceleration) * time
400 rpm = 41.89 rad/s = (ang. acc.) * t
t = 104.7 s
final linear speed = R * (final angular speed) = [(0.48 m)/2]*41.89 rad/s = 10.05 m/s, but it is OK to show two significant figures, (10 m/s)
Thanks for that.
To calculate the time of acceleration and the linear speed of the rim of the flywheel, we can use the following steps:
Step 1: Convert the final angular velocity from revolutions per minute (rpm) to radians per second (rad/s):
- Given final angular velocity = 400 rev/min
- To convert rev/min to rad/s, we multiply by 2π/60 (since 1 rev = 2π radians and 1 min = 60 s):
final angular velocity = (400 rev/min) * (2π/60) = 41.89 rad/s
Step 2: Use the formula relating angular acceleration, time, and final angular velocity:
- We are given the initial angular velocity is 0 (since the flywheel starts from rest).
- The formula is: final angular velocity = angular acceleration * time
- We can rearrange this formula to solve for time: time = final angular velocity / angular acceleration
- Plugging in the values: time = 41.89 rad/s / 0.4 rad/s^2 = 104.7 s
Hence, your answer for part (a), the time of acceleration, is correct: 104.7 s.
Step 3: Calculate the linear speed of the rim of the flywheel:
- The linear speed is the product of the radius and the final angular velocity.
- The radius of the flywheel is given as 480 mm, which we should convert to meters by dividing by 1000: radius = 480 mm / 1000 = 0.48 m
- The linear speed = radius * final angular velocity = 0.48 m * 41.89 rad/s = 20.0912 m/s
- Rounding this to two significant figures, we get the final answer of 20 m/s.
Hence, your answer for part (b), the linear speed of the rim of the flywheel, should be 20 m/s instead of 10 m/s.
So, the correct answers are:
a) The time of acceleration = 104.7 s
b) The linear speed of the rim of the flywheel = 20 m/s
I hope this clears up any confusion and helps you understand the problem and the solution better.