Prove that a unit speed curve with k and tour constant is a helix circular. unit...
please prove Q9....
9. If α is a curve with K > 0 and τ both constant, show that α is a circular helix
9. If α is a curve with K > 0 and τ both constant, show that α is a circular helix
please prove Q9....
9. If α is a curve with K > 0 and τ both constant, show that α is a circular helix
4.25. Combine the previous result with Proposition 4.10 to prove that if a(s) is a unit speed curve with K,-0, τ 0, then α(s) lies on a sphere if and only if τ/K- . (K7sK')' (or τρ-:-(p'/t)'). PROPOSITION 4.10. Let α(s) be a unit speed curve 0. If τ whose lies sphere on a image 0, then of radius r and center m. Then K where ρ :-1/K and σ-1/τ. Hence rz-
4.25. Combine the previous result with Proposition 4.10...
please solve Q7....
7. Let ㏄ 1 → R, be a cylindrical helix with unit vector u. For to E 1, the curve is called a cross-sectional curve of the cylinder on which α lies Prove (a) γ lies in the plane through o(to) orthogonal to u. (b) The curvature of γ is dsin't, where κ is the curvature of α.
7. Let ㏄ 1 → R, be a cylindrical helix with unit vector u. For to E 1, the...
A car moving with a constant speed of 85 km/h enters a circular, flat curve with a radius of curvature of 0.40 km. If the friction between the road and the car’s tires can support a centripetal acceleration of 1.25 m/s2, without slipping, does the car navigate the curve safely, or does it fly off the road?
2. Let (a, b) nonvanishing. Denote the Frenet frame by {T, N, B} vector a E R3 with R3 be smooth with = 1 and curvature k and torsion r, both Assume there exists a unit Ta constant = COS a. circular helix is an example of such curve a) Show that b) Show that N -a 0. c) Show that k/T =constant ttan a
2. Let (a, b) nonvanishing. Denote the Frenet frame by {T, N, B} vector a...
The car travels along the circular curve of radiusr 400 ft with a constant speed of U = 30 ft/s .(Figure 1) ▼ Part A Determine the angular rate of rotation θ of the radial line r Express your answer with the appropriate units. Figure 1 of 1 Value Units Submit Request Answer ▼ Part B r=400 ft Determine the magnitude of the car's acceleration Express your answer with the appropriate units. a= 1 Value 1 Units
A car is going along a circular road at a constant speed. The radius of the curve is 290 m, and the car takes 1.7 minutes to complete one round. Calculate its centripetal acceleration in m/s2.
Let B: I + R3 be a unit speed curve. Let X be the vector field along ß defined by X = TT + KB. Prove that T' = X XT, N' = X X N, B' = X B.
Car A is traveling at the constant speed of 61 km/h as it rounds the circular curve of 285-m radius and at the instant represented is at the position 8 46°. Car B is traveling at the constant speed of 81 km/h and passes the center of the circle at this same instant. Car A is located with respect to car B by polar coordinates r and with the pole moving with B For this instant determine the values of...