A car is moving on road with speed 54km per hour . What should be the value of torque if the car is brought to rest in 15 seconds? Radius and moment of inertia of wheel about the axis of rotation are 0.35 and 3km m^2 respectively.
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Given:
initial velocity(linear)=v1=54kmph=54x5/18=15m/s
Radius of wheel=r1=0.35m
time=t=15sec
Initial angular velocity =ω1=v1/r1
⇒15/0.35
⇒1500/35
⇒42.9 rad/s
final angular velocity=ω2=0 [∵ car is brought to rest]
Inertia=I=3kgm²
Angular acceleration =α=ω2-ω1/t
⇒(0-42.9)/15
⇒-42.9/15
⇒-2.86 rad/s²
Torque =τ=Ια
⇒3x(-2.86)
-8.58 N.M
initial velocity(linear)=v1=54kmph=54x5/18=15m/s
Radius of wheel=r1=0.35m
time=t=15sec
Initial angular velocity =ω1=v1/r1
⇒15/0.35
⇒1500/35
⇒42.9 rad/s
final angular velocity=ω2=0 [∵ car is brought to rest]
Inertia=I=3kgm²
Angular acceleration =α=ω2-ω1/t
⇒(0-42.9)/15
⇒-42.9/15
⇒-2.86 rad/s²
Torque =τ=Ια
⇒3x(-2.86)
-8.58 N.M
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