Question

Angular velocity of the motor is 300 rad/sec. Find velocity of wheel for a diameter of
0.3 m and gear ratio of 5

Answer 1

Question

Angular velocity of a motor is 300 rad/s . Find the linear velocity for a diameter of 0.3 m

Solution

• Velocity of the motor is 45 m/s

From the Question,

• Angular Velocity = 300 rad/s

• Diameter,d = 0.3 m

• Radius,r = 0.15 m

Angular Velocity

The rate of change of angular displacement is known as Angular Velocity

From the definition,

$\sf \: \omega \: = \dfrac{d \theta}{dt}$

Angle At The Centre = Arc Length/Radius

$\longrightarrow \: \sf \: \omega \: = \dfrac{1}{r} \: \times \dfrac{ds}{dt} \\ \\ \longrightarrow \: \boxed{ \boxed{\sf \: v = r \omega}}$

Substituting the values,we get :

$\longrightarrow \: \sf \: v =(0.15)(300) \\ \\ \longrightarrow \: \sf \: v = \dfrac{15}{100} \times 300 \\ \\ \huge{\longrightarrow \: \boxed{ \boxed{ \sf \: v = 45 \: {ms}^{ - 1} }}}$

Answer 2

$\huge{\underline{\underline{\red{\mathfrak{AnSwEr :}}}}}$

Given :

• Angular velocity (ω) = 300 rad/s
• Radius = Diameter/2 = 0.15 m

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To Find :

• Velocity of wheel

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Solution :

Use relation between angular velocity and velocity.

$\large{\boxed{\sf{v \: = \: r \omega}}} \\ \\ \implies {\sf{v \: = \: 0.15 \: \times \: 300}} \\ \\ \implies {\sf{v \: = \: 45}} \\ \\ {\underline{\sf{\therefore \: Velocity \: of \: wheel \: is \: 45 \: ms^{-1}}}}$