A constant force of 20N is applied tangentially to a string wound on the rim of a 40 cm diameter wheel, initially at rest.

(i) How much work does this force do as it turns the wheel through 45„a?
(3 %)
(ii) If the wheel has mass 8.0 kg and radius of gyration 15 cm, how long does it take the wheel to rotate through this angle?

(i) 20N * 0.2 m * (angle in radians).

I cannot interpret your angle symbol, which shows up here as ,,a.

(ii) Angular acceleration rate = (Torque)/(Moment of inertia)
= (Torque)/[(Mass)*Rg^2]
The torque is 4 N*m
Angular acceleration =
4 N*m/(8*.15^2 kg m^2) = 22.2 rad/s^2

Time required to rotate angle theta =
2*(theta)/(angular acceleration rate)

so for the first part 20N * 0.2m * 2pi is that correct?

also how did you get your torque?

(iii) What is the angular momentum of the wheel after this time?

You never said the angle turned was 2 pi. You typed 45,,a

Torque is force times lever arm (in this case, wheel radius)

(iii) Angular momentum after time T is
(Torque)*(Time) =
(Moment of inertia)*(angular velocity)

no i mean to convert 45degrees into rads you multiply by 2pi

thanks for your help

45 degrees is pi/4 radians. You multiply by pi/180 radians per degree, NOT 2 pi

how did u find the angular velocity?

im tryin to use v = wr but i don't know where to find the normal velocity of the rim

To solve this problem, we need to use the concepts of work and rotational dynamics. Let's break down each part of the question and explain how to get the answers step by step:

(i) How much work does this force do as it turns the wheel through 45°?

To calculate the work done by a force applied tangentially to a rotating object, we use the formula:

Work = Force * Distance * cos(θ)

In this case, the force is 20N and the angle turned is 45°.

However, we need to calculate the distance that the point of application of the force moves as the wheel rotates. To do this, we need to find the circumference of the wheel.

Circumference = π * diameter
Circumference = π * 40 cm

So, the distance traveled is given by:

Distance = (angle in radians) * radius
Distance = (45° * π/180) * (40 cm/2)

Now, we can substitute the values into the work formula to find the work done:

Work = 20N * [(45° * π/180) * (40 cm/2)] * cos(45°)

Solving this expression will give us the answer.

(ii) If the wheel has a mass of 8.0 kg and a radius of gyration of 15 cm, how long does it take for the wheel to rotate through this angle?

To find the time it takes for the wheel to rotate through a given angle, we can use the formula:

Time = (angle in radians) * inertia / (force * radius)

The angle is again 45°, the inertia is given by:

Inertia = mass * (radius of gyration)^2

And the force is still 20N.

Putting in these values, we can calculate the time it takes for the wheel to rotate.