Calculating Linear and Centripetal Acceleration for a Car in Rotational Motion

AI Thread Summary
To calculate the linear speed of a car in rotational motion, the formula used is linear speed equals the radius multiplied by angular speed, resulting in 30 m/s. The centripetal acceleration is determined using the formula rw², yielding a value of 18 m/s². The linear acceleration, calculated as r multiplied by angular acceleration, is 10 m/s². The total linear acceleration combines both components, resulting in approximately 20.6 m/s². Understanding the vector nature of acceleration is crucial for accurately determining the total acceleration in different directions.
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Homework Statement


At a particular moment in a race, a car moving around a turn with a radius of 50m had an angular speed of .6rad/sec and an angular acceleration of .2rad/sec2
At this particular moment find:
the linear speed
the centripetal acceleration
its total linear acceleration


Homework Equations


w=\Deltatheta/\Deltat
vt=rw
alpha=\Deltaw/\Deltat


The Attempt at a Solution

linearspeed =50*.6=30m/s
linear acceleration would be at=r(alpha) so at=10m/s2
I don't know how to calculate the centripetal acceleration
 
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pb23me said:
At this particular moment find:
...
the centripetal acceleration
its total linear acceleration
...
linear acceleration would be at=r(alpha) so at=10m/s2
I don't know how to calculate the centripetal acceleration
You probably have a formula for centripetal acceleration in your book or notes. This is one of those "given" formulas that you learn (on par with F=m.a in freshman physics). Your other problem is, what do you really mean by "linear acceleration"? Acceleration, like velocity, has a magnitude and direction, i.e. it is a vector. As a vector, it can be broken into components and there is some "resultant" or "total" acceleration. Hint: what is the relationship between the "centripetal" direction, and the direction that you have indicated with a subscript "t"? Identify the components of the acceleration in an appropriate coordinate system.
 
ok so centripetal acceleration=rw2=18m/s2
i know that centripetal acceleration points towards the center of the circle and linear acceleration is tangential to the circle... i don't know what direction to break linear acceleration up into..
 
well i just looked at the drawing and it seems to indicate that there is an acceleration 45 degrees inward from at
 
102+182=424 so total linear acceleration=20.6m/s2
 
Thread 'Variable mass system : water sprayed into a moving container'

Thread 'Variable mass system : water sprayed into a moving container'

Starting with the mass considerations #m(t)# is mass of water #M_{c}# mass of container and #M(t)# mass of total system $$M(t) = M_{C} + m(t)$$ $$\Rightarrow \frac{dM(t)}{dt} = \frac{dm(t)}{dt}$$ $$P_i = Mv + u \, dm$$ $$P_f = (M + dm)(v + dv)$$ $$\Delta P = M \, dv + (v - u) \, dm$$ $$F = \frac{dP}{dt} = M \frac{dv}{dt} + (v - u) \frac{dm}{dt}$$ $$F = u \frac{dm}{dt} = \rho A u^2$$ from conservation of momentum , the cannon recoils with the same force which it applies. $$\quad \frac{dm}{dt}...
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