Question

The angular displacement of a body is a function of time and is given by equation :
θ = 10 + 3 t + 6 t2, where t is in seconds. Determine the angular velocity, displacement and acceleration when t = 5 seconds. State whether or not it is a case of uniform angular acceleration

Answer 1

The angular displacement of a body is a function of time and is given by equation, θ = 10 + 3t + 6t², where t is in seconds.

we have to find angular velocity, displacement and acceleration when t = sec.

angular velocity is the rate of change of angular displacement with respect to time.

angular velocity, dθ/dt = d(10 + 3t + 6t²)/dt

= 3 + 12t

at t = 5 sec

angular velocity, ω = 3 + 12 × 5 = 63 rad/s

angular displacement, θ = 10 + 3t + 6t²

= 10 + 3 × 5 + 6 × 5²

= 10 + 15 + 150

= 175 rad

angular acceleration is the rate of change of angular velocity with respect to time.

angular acceleration, α = dω/dt = d(3 + 12t)/dt

= 12 rad/s² [ constant ]

as angular velocity is constant so, it is a case of uniform angular acceleration.