{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

11_InstSolManual_PC

# 11_InstSolManual_PC - ROTATIONAL VECTORS AND ANGULAR...

This preview shows pages 1–3. Sign up to view the full content.

ROTATIONAL VECTORS AND ANGULAR MOMENTUM E XERCISES Section 11.1 Angular Velocity and Acceleration Vectors 12. If we assume that the wheels are rolling without slipping (see Section 10.5), the magnitude of the angular velocity is 1 cm v / (70 m/3.6 s)/(0.31 m) 62.7 s . r ϖ - = = = With the car going north, the axis of rotation of the wheels is east-west. Since the top of a wheel is going in the same direction as the car, the right-hand rule gives the direction of ϖ as west. 13. I NTERPRET The problem asks about the angular acceleration of the wheels as the car traveling north with a speed of 70 km/h makes a 90 ° left turn that lasts for 25 s. D EVELOP The speed of the car is cm 70 km/h 19.4 m/s. v = = Assuming that the wheels are rolling without slipping, the magnitude of the initial angular velocity is cm 19.4 m/s 62.7 rad/s 0.31 m v r ϖ = = = With the car going north, the axis of rotation of the wheels is east-west. Since the top of a wheel is going in the same direction as the car, the right-hand rule gives the direction of i ϖ r as west. In unit-vector notation, we write ˆ . i i ϖ ϖ = - r After making a left turn, the angular speed remains unchanged, but the direction of f ϖ r is now south (see sketch). In unit-vector notation, we write ˆ . f j ϖ ϖ = - r E VALUATE Using Equation 10.4, we find the angular acceleration to be av ˆ ˆ ( ) ˆ ˆ ( ) f i j i i j t t t t ϖ ϖ ϖ ϖ ϖ ϖ α - - - - = = = = - r r r r The magnitude of av α r is 2 av 2 2(62.7 rad/s) | | 3.55 rad/s 25 s t ϖ α = = = r and av α r points in the south-east direction (in the direction of the vector ˆ ˆ ). i j - A SSESS Angular acceleration av α r points in the same direction as . ϖ r 14. Suppose that the x -axis is horizontal in the direction of the final angular velocity ˆ ( (60 rpm) ) f i = ϖ and the y -axis is vertical in the direction of the initial angular velocity ˆ ˆ ( (45 rpm) ). j = i ϖ Equation 11.1 implies that av ( )/ f i t = - ∆ = α ϖ ϖ ˆ ˆ ˆ ˆ (60 45 ) rpm/15 s (4 3 ) rpm/s. i j i j = - - Its magnitude is 2 2 av (4) ( 3) rpm/s α = + - = 2 2 5 rpm/s 5( /30) s 0.524 s , π - - = = at an angle 1 3 4 tan ( ) 36.9 θ - = - = - ° to the x axis (i.e., below the horizontal). 11.1 11

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document