A rigid object is rotating such that its angular position changes with time according to the equation
Θ(t)=(3.00t2−2.00t+3.00)rad ,where t is in seconds.
a) What is the tangential speed at t=2.00s and at 3.00 sec.
b) What is the tangential acceleration and the centripetal acceleration at t = 2.00s
I don't understand how to get these the formulas given in the text state:
vt = r omega (tangential speed)
at = r alpha (tangential acceleration)
ac = r omega^2 (centripetal acceleration)
all these equations require the knowledge of the radius but that was not given.
Can someone map out how i'd answer these questions?
Θ(t)=(3.00t2−2.00t+3.00)rad ,where t is in seconds.
a) What is the tangential speed at t=2.00s and at 3.00 sec.
b) What is the tangential acceleration and the centripetal acceleration at t = 2.00s
I don't understand how to get these the formulas given in the text state:
vt = r omega (tangential speed)
at = r alpha (tangential acceleration)
ac = r omega^2 (centripetal acceleration)
all these equations require the knowledge of the radius but that was not given.
Can someone map out how i'd answer these questions?
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You are correct - you must have the radius. If you are not told it, state that you are assuming that it is constant and equal to R metres. Then give your answers in terms of R.
θ = 3t² - 2t + 3
ω = dθ/dt = 6t - 2
a)
vt = ωR
When t = 2s, vt = (6x2 - 2)R = 10R m/s
When t = 3s, vt = (6x3 - 2)R = 16R m/s
b)
α = dω/dt = 6 rad/s²
at = Rα = 6R m/s². This is constant so is the value when t=2s as well as at all other times.
ac = Rω²
When t=2s, ω = 6x2 - 2 = 10rad/s
ac = R x 10² = 100R m/s²
θ = 3t² - 2t + 3
ω = dθ/dt = 6t - 2
a)
vt = ωR
When t = 2s, vt = (6x2 - 2)R = 10R m/s
When t = 3s, vt = (6x3 - 2)R = 16R m/s
b)
α = dω/dt = 6 rad/s²
at = Rα = 6R m/s². This is constant so is the value when t=2s as well as at all other times.
ac = Rω²
When t=2s, ω = 6x2 - 2 = 10rad/s
ac = R x 10² = 100R m/s²