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Answer:
The current is increasing at a rate of 0.32 ampere per second.
Explanation:
The voltage of the resistor is modelled after Ohm's Law, which states that voltage is directly proportional to current:
(1)
Where:
- Voltage, measured in volts.
- Current, measured in amperes.
- Resistance, measured in ohms.
An expression for the rate of change in voltage is found by Differential Calculus:
(2)
Where:
- Rate of change in voltage, measured in volts per second.
- Rate of change in current, measured in amperes per second.
- Rate of change in resistance, measured in ohms per second.
If we know that ,
,
and
, then the rate of change in current is:
(3)
The current is increasing at a rate of 0.32 ampere per second.
Answer:
a_total = 2 √ (α² + w⁴) , a_total = 2,236 m
Explanation:
The total acceleration of a body, if we use the Pythagorean theorem is
a_total² = a_T²2 + ²
where
the centripetal acceleration is
a_{c} = v² / r = w r²
tangential acceleration
a_T = dv / dt
angular and linear acceleration are related
a_T = α r
we substitute in the first equation
a_total = √ [(α r)² + (w r² )²]
a_total = 2 √ (α² + w⁴)
Let's find the angular velocity for t = 2 s if we start from rest wo = 0
w = w₀ + α t
w = 0 + 1.0 2
w = 2.0rad / s
we substitute
a_total = r √(1² + 2²) = r √5
a_total = r 2,236
In order to finish the calculation we need the radius to point A, suppose that this point is at a distance of r = 1 m
a_total = 2,236 m