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UNO [17]
1 year ago
10

Please help me with this rotation and linear motion problem

Physics
1 answer:
kirill115 [55]1 year ago
5 0

The initial angular velocity of the wheel would be 15.5 rad/s

<h3>What is Velocity?</h3>

The total displacement covered by any object per unit of time is known as velocity. It depends on the magnitude as well as the direction of the moving object. The unit of velocity is meter/second.

The relation between the linear velocity and the angular velocity

V= ωr

as given the initial  linear velocity is 8.22 m/s

the radius of the wheel is 0.530 m

By substituting the value of the linear velocity and the radius

8.22 = 0.530ω

ω = 8.22/0.530

ω = 15.5 rad/s

Thus, the initial angular velocity of the wheel comes out to be  15.5 rad/s

Learn more about Velocity from here

brainly.com/question/18084516

#SPJ1

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11. A vector M is 15.0 cm long and makes an angle of 20° CCW from x axis and another vector N is 8.0 cm long and makes an angle
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Answer:

The magnitude of the resultant vector is 22.66 cm and it has a direction of 29.33°

Explanation:

To find the resultant vector, you first calculate x and y components of the two vectors M and N. The components of the vectors are calculated by using cos and sin function.

For M vector you obtain:

M=M_x\hat{i}+M_y\hat{j}\\\\M=15.0cm\ cos(20\°)\hat{i}+15.0cm\ sin(20\°)\hat{j}\\\\M=14.09cm\ \hat{i}+5.13\ \hat{j}

For N vector:

N=N_x\hat{i}+N_y\hat{j}\\\\N=8.0cm\ cos(40\°)\hat{i}+8.0cm\ sin(40\°)\hat{j}\\\\N=6.12cm\ \hat{i}+5.142\ \hat{j}

The resultant vector is the sum of the components of M and N:

F=(M_x+N_x)\hat{i}+(M_y+N_y)\hat{j}\\\\F=(14.09+6.12)cm\ \hat{i}+(5.13+5.142)cm\ \hat{j}\\\\F=20.21cm\ \hat{i}+10.27cm\ \hat{j}

The magnitude of the resultant vector is:

|F|=\sqrt{(20.21)^2+(10.27)^2}cm=22.66cm

And the direction of the vector is:

\theta=tan^{-1}(\frac{10.27}{20.21})=29.93\°

hence, the magnitude of the resultant vector is 22.66 cm and it has a direction of 29.33°

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Answer:

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