A child is pushing a merry-go-round. The angle through which the merry-go- round has turned varies with time according to 0(t)=yt + Bt³, where 7=0.390 rad/s and B=0.0130 rad/s². For related problem-solving tips and strategies, you may want to view a Video Tutor Solution of Calculating angular velocity. Part A Calculate the angular velocity of the merry-go-round as a function of time. Express your answer in terms of the variables,, and rad/s. [5] ΑΣΦ w₁(t) = ?
Angular Momentum
The momentum of an object is given by multiplying its mass and velocity. Momentum is a property of any object that moves with mass. The only difference between angular momentum and linear momentum is that angular momentum deals with moving or spinning objects. A moving particle's linear momentum can be thought of as a measure of its linear motion. The force is proportional to the rate of change of linear momentum. Angular momentum is always directly proportional to mass. In rotational motion, the concept of angular momentum is often used. Since it is a conserved quantity—the total angular momentum of a closed system remains constant—it is a significant quantity in physics. To understand the concept of angular momentum first we need to understand a rigid body and its movement, a position vector that is used to specify the position of particles in space. A rigid body possesses motion it may be linear or rotational. Rotational motion plays important role in angular momentum.
Moment of a Force
The idea of moments is an important concept in physics. It arises from the fact that distance often plays an important part in the interaction of, or in determining the impact of forces on bodies. Moments are often described by their order [first, second, or higher order] based on the power to which the distance has to be raised to understand the phenomenon. Of particular note are the second-order moment of mass (Moment of Inertia) and moments of force.
![A child is pushing a merry-go-round. The angle through which the merry-go-
round has turned varies with time according to 0(t)=yt + Bt³, where
7=0.390 rad/s and B=0.0130 rad/s³.
For related problem-solving tips and strategies, you may want to view a Video
Tutor Solution of Calculating angular velocity.
Part A
Calculate the angular velocity of the merry-go-round as a function of time.
Express your answer in terms of the variables,, and rad/s.
[5] ΑΣΦ
w₁(t) =
?](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F76eec8ec-d87c-4fdd-96a3-96e8325f09a2%2Fc0a23f4c-0073-42c6-b8a6-debbe6020157%2Fnm4ruv8_processed.jpeg&w=3840&q=75)
![At t = 0 a grinding wheel has an angular velocity of 21.0 rad/s. It has a
constant angular acceleration of 30.0 rad/s² until a circuit breaker trips at time
t=2.10 s. From then on, it turns through an angle 439 rad as it coasts to a stop
at constant angular acceleration.
▼
Part A
▼
Through what total angle did the wheel turn between t= 0 and the time it stopped?
Express your answer in radians.
G] ΑΣΦ
0 =
Submit
▾ Part B
t=
At what time did it stop?
Express your answer in seconds.
Submit
Part C
a =
Request Answer
Submit
G
| ΑΣΦ
6
Request Answer
[5] ΑΣΦ
What was its acceleration as it slowed down?
Express your answer in radians per second squared.
S ?
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?
SMC ?
S
rad
rad/s²](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F76eec8ec-d87c-4fdd-96a3-96e8325f09a2%2Fc0a23f4c-0073-42c6-b8a6-debbe6020157%2F8ps6yrh_processed.jpeg&w=3840&q=75)
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