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A disc rotates about a fixed axis with variable angular velocity which is equal to (at+b). initially at t=0 it's angular velocity is 1rad/s and angular position is 2rad. at the instant t=2s angular velocity is 5rad/s.determine angular position and angular acceleration when t=4s.
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A disc rotates about a fixed axis with variable angular velocity which...
A disc rotates about fixed axis its angular velocity varies with time w=at+b initially at t=0 w= 1 rad/s
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A disc rotates about a fixed axis with variable angular velocity which...
Given data:
- Initial angular velocity (ω) = 1 rad/s
- Initial angular position (θ) = 2 rad
- Angular velocity at t = 2s (ω') = 5 rad/s
- Time (t) = 4s
Using the formula:
θ = θ₀ + ω₀t + 0.5αt²
where,
θ = angular position at time t
θ₀ = initial angular position
ω₀ = initial angular velocity
α = angular acceleration
t = time
Finding angular position at t = 4s:
Using the formula, we can find the angular position at time t = 4s.
θ = θ₀ + ω₀t + 0.5αt²
θ = 2 + (1)(4) + 0.5α(4)²
θ = 2 + 4 + 8α
θ = 6 + 8α
Finding angular acceleration:
To find the angular acceleration at t = 4s, we need to use another formula:
ω' = ω₀ + αt
where,
ω' = angular velocity at time t
ω₀ = initial angular velocity
α = angular acceleration
t = time
Substituting the given values:
5 = 1 + α(4)
5 - 1 = 4α
4 = 4α
α = 1 rad/s²
Substituting the values in the equation for angular position:
θ = 6 + 8α
θ = 6 + 8(1)
θ = 6 + 8
θ = 14 rad
Final Result:
- Angular position at t = 4s is 14 rad.
- Angular acceleration at t = 4s is 1 rad/s².
- Initial angular velocity (ω) = 1 rad/s
- Initial angular position (θ) = 2 rad
- Angular velocity at t = 2s (ω') = 5 rad/s
- Time (t) = 4s
Using the formula:
θ = θ₀ + ω₀t + 0.5αt²
where,
θ = angular position at time t
θ₀ = initial angular position
ω₀ = initial angular velocity
α = angular acceleration
t = time
Finding angular position at t = 4s:
Using the formula, we can find the angular position at time t = 4s.
θ = θ₀ + ω₀t + 0.5αt²
θ = 2 + (1)(4) + 0.5α(4)²
θ = 2 + 4 + 8α
θ = 6 + 8α
Finding angular acceleration:
To find the angular acceleration at t = 4s, we need to use another formula:
ω' = ω₀ + αt
where,
ω' = angular velocity at time t
ω₀ = initial angular velocity
α = angular acceleration
t = time
Substituting the given values:
5 = 1 + α(4)
5 - 1 = 4α
4 = 4α
α = 1 rad/s²
Substituting the values in the equation for angular position:
θ = 6 + 8α
θ = 6 + 8(1)
θ = 6 + 8
θ = 14 rad
Final Result:
- Angular position at t = 4s is 14 rad.
- Angular acceleration at t = 4s is 1 rad/s².
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A disc rotates about a fixed axis with variable angular velocity which is equal to (at+b). initially at t=0 it's angular velocity is 1rad/s and angular position is 2rad. at the instant t=2s angular velocity is 5rad/s.determine angular position and angular acceleration when t=4s.
Question Description
A disc rotates about a fixed axis with variable angular velocity which is equal to (at+b). initially at t=0 it's angular velocity is 1rad/s and angular position is 2rad. at the instant t=2s angular velocity is 5rad/s.determine angular position and angular acceleration when t=4s. for NEET 2024 is part of NEET preparation. The Question and answers have been prepared according to the NEET exam syllabus. Information about A disc rotates about a fixed axis with variable angular velocity which is equal to (at+b). initially at t=0 it's angular velocity is 1rad/s and angular position is 2rad. at the instant t=2s angular velocity is 5rad/s.determine angular position and angular acceleration when t=4s. covers all topics & solutions for NEET 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A disc rotates about a fixed axis with variable angular velocity which is equal to (at+b). initially at t=0 it's angular velocity is 1rad/s and angular position is 2rad. at the instant t=2s angular velocity is 5rad/s.determine angular position and angular acceleration when t=4s..
A disc rotates about a fixed axis with variable angular velocity which is equal to (at+b). initially at t=0 it's angular velocity is 1rad/s and angular position is 2rad. at the instant t=2s angular velocity is 5rad/s.determine angular position and angular acceleration when t=4s. for NEET 2024 is part of NEET preparation. The Question and answers have been prepared according to the NEET exam syllabus. Information about A disc rotates about a fixed axis with variable angular velocity which is equal to (at+b). initially at t=0 it's angular velocity is 1rad/s and angular position is 2rad. at the instant t=2s angular velocity is 5rad/s.determine angular position and angular acceleration when t=4s. covers all topics & solutions for NEET 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A disc rotates about a fixed axis with variable angular velocity which is equal to (at+b). initially at t=0 it's angular velocity is 1rad/s and angular position is 2rad. at the instant t=2s angular velocity is 5rad/s.determine angular position and angular acceleration when t=4s..
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